3. Functions

Intro to Functions & Their Graphs

3. Functions

Intro to Functions & Their Graphs

Guided videos.

Learn with Nick

Go to the course

5:20

Relations and Functions

Verifying if Equations are Functions

Relations & Functions Example 1

Finding the Domain and Range of a Graph

Finding the Domain of an Equation

Showing 5 of 5 videos

Practice this topic

Multiple Choice

State the inputs and outputs of the following relation. Is it a function? { $\left(-3,5\right),\left(0,2\right),\left(3,5\right)$ }

State the inputs and outputs of the following relation. Is it a function? { $\left(2,5\right),\left(0,2\right),\left(2,9\right)$ }

Is the equation $y=-2x+10$ a function? If so, rewrite it in function notation and evaluate at $f\left(3\right)$ .

Is the equation $y^2+2x=10$ a function? If so, rewrite it in function notation and evaluate at $f\left(-1\right)$ .

Find the domain and range of the following graph (write your answer using interval notation).

Find the domain of $f\left(x\right)=\sqrt{x+4}$ . Express your answer using interval notation.

Find the domain of $f\left(x\right)=\frac{1}{x^2-5x+6}$ . Express your answer using interval notation.

In Exercises 1–30, find the domain of each function. f(x)=3(x-4)

941

views

Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ-g)(2)

330

views

Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ∘g)(2)

338

views

Textbook Question

In Exercises 1–30, find the domain of each function. g(x) = 3/(x^2-2x-15)

824

views

Textbook Question

In Exercises 1–30, find the domain of each function. f(x) = 1/(x+7) + 3/(x-9)

431

views

Textbook Question

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ+g)(-5)

389

views

Textbook Question

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ-g)(4)

313

views

Textbook Question

In Exercises 1–30, find the domain of each function. f(x) = √(x - 3)

363

views

Textbook Question

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ/g)(5)

315

views

Textbook Question

In Exercises 1–30, find the domain of each function. f(x) = 1/√(x - 3)

325

views

Textbook Question

For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-6

312

views

Textbook Question

For the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2. ƒ(x)=2x^2-3x, g(x)=x^2-x+3

364

views

Textbook Question

For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2. ƒ(x)=2x^2-3x, g(x)=x^2-x+3

310

views

Textbook Question

For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2. ƒ(x)=√(4x-1), g(x)=1/x

315

views

Textbook Question

In Exercises 1–30, find the domain of each function. g(x) = √(x −2)/(x-5)

340

views

Textbook Question

In Exercises 1–30, find the domain of each function. f(x) = (2x+7)/(x^3 - 5x^2 - 4x+20)

348

views

Textbook Question

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

348

views

Textbook Question

In Exercises 31–50, find f/g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

371

views

Textbook Question

Use the graph to evaluate each expression. See Example 3(a). (ƒ-g)(1)

414

views

Textbook Question

In Exercises 31–50, find fg and determine the domain for each function. f(x) = x -5, g(x) = 3x²

503

views

Textbook Question

Use the graph to evaluate each expression. See Example 3(a). (ƒg)(1)

357

views

Textbook Question

In Exercises 31–50, find fg and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 17

602

views

Textbook Question

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 16

347

views

Textbook Question

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15

340

views

Textbook Question

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = √x, g(x) = x − 4

356

views

Textbook Question

In Exercises 31–50, find f/g and determine the domain for each function. f(x) = √x, g(x) = x − 4

383

views

Textbook Question

In Exercises 31–50, find ƒ-g and determine the domain for each function. f(x) = 2 + 1/x, g(x) = 1/x

338

views

Textbook Question

In Exercises 31–50, find fg and determine the domain for each function. f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)

490

views

Textbook Question

In Exercises 31–50, find f−g and determine the domain for each function. f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)

349

views

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=6x+2

338

views

Textbook Question

In Exercises 31–50, find f/g and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)

400

views

Textbook Question

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = √(x +4), g(x) = √(x − 1)

416

views

Textbook Question

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = √(x +4), g(x) = √(x − 1)

372

views

Textbook Question

In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)

400

views

Textbook Question

In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)

377

views

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=1/x^2

324

views

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=-x^2

349

views

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2+3x+1

354

views

Textbook Question

In Exercises 51–66, find a. (fog) (2) b. (go f) (2) f(x)=4x-3, g(x) = 5x² - 2

316

views

Textbook Question

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (ƒ∘g)(4)

306

views

Textbook Question

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) f(x) = x²+2, g(x) = x² – 2

305

views

Textbook Question

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) f(x) = 4-x, g(x) = 2x² +x+5

422

views

Textbook Question

In Exercises 59-64, let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. (fog) (0)

400

views

Textbook Question

In Exercises 51–66, find a. (fog) (x) b. (go f) (x). f(x) = √x, g(x) = x − 1

360

views

Textbook Question

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (ƒ∘ƒ)(2)

338

views

Textbook Question

In Exercises 59-64, let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. g (f[h (1)])

338

views

Textbook Question

In Exercises 67-74, find a. (fog) (x) b. the domain of f o g. f(x) = 2/(x+3), g(x) = 1/x

722

views

Textbook Question

In Exercises 67-74, find a. (fog) (x) b. the domain of f o g. f(x) = x/(x+1), g(x) = 4/x

614

views

Textbook Question

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=-6x+9, g(x)=5x+7

924

views

Textbook Question

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=8x+12, g(x)=3x-1

412

views

Textbook Question

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=x+3

385

views

Textbook Question

In Exercises 75-82, express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x). h(x) = ∛(x² – 9)

415

views

Textbook Question

In Exercises 76–81, find the domain of each function. g(x) = 4/(x - 7)

357

views

Textbook Question

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=x+2, g(x)=x^4+x^2-4

486

views

Textbook Question

In Exercises 75-82, express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x). h(x) = |2x-5|

389

views

Textbook Question

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=2/x, g(x)=x+1

510

views

Textbook Question

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=2/x, g(x)=x+1

1091

views

Textbook Question

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=1/(x+5)

312

views

Textbook Question

Use the graphs of f and g to solve Exercises 83–90.

Use the graphs of f and g to solve Exercises 83–90.

In Exercises 89–90, express the given function h as a composition of two functions f and g so that h(x) = (f ○ g)(x). h(x) = (x^2 + 2x - 1)^4

871

views

Textbook Question

Use the graphs of f and g to solve Exercises 83–90.

In Exercises 91–94, use the graphs of f and g to evaluate each composite function.

Let ƒ(x) = 3x^2 - 4 and g(x) = x^2 - 3x -4. Find each of the following. (f+g)(2k)

535

views

Textbook Question

Let ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (ƒ ○ g)(x)

337

views

Textbook Question

Let ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (f ○ g)(-6)

321

views

Textbook Question

Use the table to evaluate each expression, if possible. (f-g)(3)

502

views

Textbook Question

The graphs of two functions ƒ and g are shown in the figures.

Fill in the blank to correctly complete each sentence. The point (-1, 3) lies in quadrant ________ in the rectangular coordinate system.

145

views

Textbook Question

Fill in the blank to correctly complete each sentence. The point (4,_____ ) lies on the graph of the equation y = 3x - 6.

143

views

Textbook Question

Fill in the blank to correctly complete each sentence. The y-intercept of the graph of y = -2x + 6 is ________.

116

views

Textbook Question

Determine whether each statement is true or false. If false, explain why. The graph of y = x^2 + 2 has no x-intercepts.

131

views

Textbook Question

Determine whether each statement is true or false. If false, explain why. The midpoint of the segment joining (0, 0) and (4, 4) is 2.

147

views

Textbook Question

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. See Examples 2 and 5(a). P(-5,-6), Q(7,-1)

132

views

Textbook Question

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. See Examples 2 and 5(a). P(8,2), Q(3,5)

130

views

Textbook Question

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. See Examples 2 and 5(a). P(6,-2), Q(4,6)

views

Textbook Question

Determine whether the three points are the vertices of a right triangle. See Example 3. (-2,-8),(0,-4),(-4,-7)

151

views

Textbook Question

Determine whether the three points are the vertices of a right triangle. See Example 3. (-4,1),(1,4),(-6,-1)

142

views

Textbook Question

Determine whether the three points are the vertices of a right triangle. See Example 3. (-2,-5),(1,7),(3,15)

121

views

Textbook Question

Determine whether the three points are collinear. See Example 4. (0,-7),(-3,5),(2,-15)

171

views

Textbook Question

Determine whether the three points are collinear. See Example 4. (0,9),(-3,-7),(2,-19)

145

views

Textbook Question

Determine whether the three points are collinear. See Example 4. (-7,4),(6,-2),(-1,1)

132

views

Textbook Question

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b). midpoint (5, 8), endpoint (13, 10)

167

views

Textbook Question

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b). midpoint (12, 6), endpoint (19, 16)

129

views

Textbook Question

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b). midpoint (6a, 6b), endpoint (3a, 5b)

153

views

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The domain of the relation { (3,5), (4, 9), (10, 13) } is _____.

120

views

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The equation y = 4x - 6 defines a function with independent variable______ and dependent variable ________ .

132

views

Textbook Question

Fill in the blank(s) to correctly complete each sentence. For the function ƒ(x) = -4x + 2, ƒ(-2)= ______.

139

views

Textbook Question

Determine whether each relation defines a function. See Example 1. {(5,1),(3,2),(4,9),(7,8)}

125

views

Textbook Question

Determine whether each relation defines a function. See Example 1. {(8,0),(5,7),(9,3),(3,8)}

116

views

Textbook Question

Determine whether each relation defines a function. See Example 1. {(9,-2),(-3,5),(9,1)}

120

views

Textbook Question

Determine whether each relation defines a function. See Example 1. {(2,4),(0,2),(2,6)}

views

Textbook Question

Determine whether each relation defines a function. See Example 1.

views

Textbook Question

Determine whether each relation defines a function. See Example 1.

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4. {(1,1),(1,-1),(0,0),(2,4),(2,-4)}

130

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4. {(2,5),(3,7),(3,9),(5,11)}

167

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

159

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

115

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

145

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

108

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

views

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=-7/(x-5)

238

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(-3)

121

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(-2)

126

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(10)

115

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(-7/3)

130

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(1/2)

134

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(-1/4)

144

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(p)

128

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(k)

135

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(-x)

133

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(x+2)

130

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(a+4)

145

views

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(2m-3)

128

views

Textbook Question

For each function, find (a) ƒ(2) and (b) ƒ(-1).See Example 7. ƒ = {(2,5),(3,9),(-1,11),(5,3)}

126

views

Textbook Question

For each function, find (a) ƒ(2) and (b) ƒ(-1).See Example 7. ƒ = {(-1,3),(4,7),(0,6),(2,2)}

views

Textbook Question

An equation that defines y as a function of x is given. (b) Find ƒ(3). x-4y=8

132

views

Textbook Question

An equation that defines y as a function of x is given. (b) Find ƒ(3). y+2x^2=3-x

127

views

Textbook Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[0.5x]], for x=7

181

views

Textbook Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)=-[[-x]], for x=2.5

142

views

Textbook Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)=2-[[-x]], for x=3.7

127

views

Textbook Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[x/4]], for x=7

132

views

Textbook Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[3-(x/2)]], for x=1

140

views

Textbook Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)=[[x]], for x=-√2

129

views

Textbook Question

Determine whether each function is even, odd, or neither. See Example 5. ƒ(x)=-x^3+2x

140

views

Textbook Question

Determine whether each function is even, odd, or neither. See Example 5. ƒ(x)=x^5-2x^3

133

views

Textbook Question

Determine whether each function is even, odd, or neither. See Example 5. ƒ(x)=0.5x^4-2x^2+6

147

views

Textbook Question

Determine whether each function is even, odd, or neither. See Example 5. ƒ(x)=x^4-5x+8

132

views

Textbook Question

Determine whether each function is even, odd, or neither. See Example 5. ƒ(x)=x+1/x^5

132

views

Textbook Question

Determine whether each function is even, odd, or neither. See Example 5. ƒ(x)=x^4+4/x^2

131

views

Textbook Question

Determine whether each equation defines y as a function of x. x = (1/3)(y^2)

204

views

Textbook Question

Determine whether each equation defines y as a function of x. y = ±√(x-2)

142

views

Textbook Question

Let ƒ(x) = -2x^2 + 3x -6. Find each of the following. ƒ(-0.5)

128

views

Textbook Question

Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. 5y^2 + 5x^2 =30

200

views

Textbook Question

Consider the following nonlinear system. Work Exercises 75 –80 in order. y = | x - 1 | y = x^2 - 4 Use the definition of absolute value to write y = | x - 1 | as a piecewise-defined function.

114

views

Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. 2x+3y=5

118

views

Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. y=-x^2

106

views

Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. y=x^2

views

Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. y=|x+4|

136

views

Textbook Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

109

views

Textbook Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.

119

views

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. x=y^4

117

views

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=-6x+4

108

views

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. x-y<4

106

views

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=-√x

105

views

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=√(7-2x)

114

views

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y=2/(x-3)

126

views

Textbook Question

Determine the largest open intervals of the domain over which each function is (a) increasing. See Example 9.

134

views

Textbook Question

Determine the largest open intervals of the domain over which each function is (c) constant. See Example 9.

116

views

Textbook Question

For each function graphed, give the minimum and maximum values of ƒ(x) and the x-values at which they occur.

112

views

Textbook Question

For each function graphed, give the minimum and maximum values of ƒ(x) and the x-values at which they occur.

130

views

Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x^2? What is its domain?

125

views

Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x^3? What is its range?

108

views

Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=|x|? What is the function value when x=1.5?

106

views

Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=∛x? Is there any open interval over which the function is decreasing?

101

views

Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=√x? What is its domain?

100

views

Textbook Question

Determine the intervals of the domain over which each function is continuous. See Example 1.

136

views

Textbook Question

Determine the intervals of the domain over which each function is continuous. See Example 1.

138

views

Textbook Question

Determine the intervals of the domain over which each function is continuous. See Example 1.

127

views

Textbook Question

Determine the intervals of the domain over which each function is continuous. See Example 1.

110

views

Textbook Question

Determine the intervals of the domain over which each function is continuous. See Example 1.

views

Textbook Question

Graph each piecewise-defined function. See Example 2. ƒ(x)={x-1 if x≤3, 2 if x>3

109

views

Textbook Question

Graph each piecewise-defined function. See Example 2. ƒ(x)={4-x if x<2, 1+2x if x≥2

111

views

Textbook Question

Graph each piecewise-defined function. See Example 2. ƒ(x)={2x+1 if x≥0, x if x<0

115

views

Textbook Question

Graph each piecewise-defined function. See Example 2. ƒ(x)={-3 if x≤1, -1 if x>1

137

views

Textbook Question

Graph each piecewise-defined function. See Example 2. ƒ(x)={-2x if x<-3, 3x-1 if -3≤x≤2, -4x if x>2

119

views

Textbook Question

Graph each piecewise-defined function. See Example 2. ƒ(x)={x^3+5 if x≤0, -x^2 if x<0

105

views

Textbook Question

Graph each piecewise-defined function. See Example 2. ƒ(x)={-(1/2)x^2+2 if x≤2, (1/2)x if x>2

views

Textbook Question

Give a rule for each piecewise-defined function. Also give the domain and range.

118

views

Textbook Question

Give a rule for each piecewise-defined function. Also give the domain and range.

169

views

Textbook Question

Give a rule for each piecewise-defined function. Also give the domain and range.

110

views

Textbook Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)={5 if 02, for x=5.6

109

views

Textbook Question

Find the value of the function for the given value of x. See Example 3. ƒ(x)={3 if 04, for x=6.2

106

views

Textbook Question

Graph each function. Give the domain and range. See Example 3. ƒ(x)=-[[x]]

113

views

Textbook Question

Graph each function. Give the domain and range. See Example 3. g(x)=[[2x-1]]

100

views

Textbook Question

Solve each problem. See Example 4. Suppose that the cost of mailing a letter weighing x ounces, where x>0, is ƒ(x)=55-15[[1-x]]cents. What is the cost for the first ounce?

views

Textbook Question

Solve each problem. See Example 4. Suppose that the cost of mailing a letter weighing x ounces, where x>0, is ƒ(x)=55-15[[1-x]]cents. What is the cost of mailing a 2.6-ounce letter?

views

Textbook Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

123

views

Textbook Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

127

views

Textbook Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

views

Textbook Question

For each graph, determine whether y is a function of x. Give the domain and range of each relation.

158

views

Textbook Question

Use a graphing calculator to graph each equation in the standard viewing window. 3x + 4y = 6

103

views

Textbook Question

Graph each equation. 2x +5y = 20

views

Textbook Question

Graph each equation. 3y = x

159

views

Textbook Question

Graph each equation. ƒ(x) = x

157

views

Textbook Question

Use a graphing calculator to graph each equation in the standard viewing window. -2x + 5y = 10

110

views

Textbook Question

Graph each equation. x - 4y = 8

views

Textbook Question

Graph each equation. x = -5

141

views

Textbook Question

Graph each equation. ƒ(x) = 3

165

views

Textbook Question

Graph each function. ƒ(x) = -|x|

114

views

Textbook Question

Graph each function. ƒ(x) = |x| -3

views

Textbook Question

Graph each function. ƒ(x) = 2∛(x+1)-2

136

views

Textbook Question

Graph each function. ƒ(x) = {|x| if x < 3 , 6-x if x ≥ 3}

115

views

Textbook Question

Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. y^3 = x + 4

104

views

Textbook Question

Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. |x| = |y|

106

views

Textbook Question

In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = x, g(x) = x + 3

In Exercises 65–70, use the graph of f to find each indicated function value. f(-3)

203

views

Textbook Question

In Exercises 65–70, use the graph of f to find each indicated function value. f(4)

views

Textbook Question

In Exercises 65–70, use the graph of f to find each indicated function value.

In Exercises 77–92, use the graph to determine a.the x-intercepts, if any; b. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

107

views

Textbook Question

In Exercises 77–92, use the graph to determine a.the x-intercepts, if any; b. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

123

views

Textbook Question

In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; and e. the missing function values, indicated by question marks, below each graph.

121

views

Textbook Question

In Exercises 49–56, identify each equation without completing the square. 4x^2 + 4y^2 + 12x + 4y + 1 = 0

122

views

Textbook Question

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+3x+5y+9/4=0

128

views

Textbook Question

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² − x + 2y + 1 = 0

128

views

Textbook Question

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² - 6y -7=0

120

views

Textbook Question

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² - 2x + y² – 15 = 0

124

views

Textbook Question

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+8x-2y-8=0

132

views

Textbook Question

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² – 10x – 6y – 30 = 0

141

views

Textbook Question

In Exercises 53–64, complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y²+6x+2y+6 = 0

133

views

Textbook Question

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x + 1)² + y² = 25

130

views

Textbook Question

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. x² + (y − 1)² = 1

136

views

Textbook Question

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x + 2)² + (y - 2)² = 4

125

views

Textbook Question

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x+3)² + (y + 2)² = 4

131

views

Textbook Question

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x − 3)² + (y + 1)² = 36

137

views

Textbook Question

In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. x² + y² = 16

150

views

Textbook Question

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (-4, 0), r = 10

133

views

Textbook Question

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (−3, −1), r = √3

127

views

Textbook Question

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (-1, 4), r = 2

150

views

Textbook Question

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (3, 2), r = 5

151

views

Textbook Question

In Exercises 31–40, write the standard form of the equation of the circle with the given center and radius. Center (0, 0), r = 7

132

views

Textbook Question

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (√50, −6) and (√2, 6)

161

views

Textbook Question

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (7√3, −6) and (3√3, −2)

148

views

Textbook Question

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (8, 3√5) and (−6, 7√5)

124

views

Textbook Question

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (-3, -4) and (6, −8)

141

views

Textbook Question

In Exercises 65-66, a line segment through the center of each circle intersects the circle at the points shown. a. Find the coordinates of the circle's center. b. Find the radius of the circle. c. Use your answers from parts (a) and (b) to write the standard form of the circle's equation.

146

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-1/4, -1/7) and (3/4, 6/7)

129

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (7/3, 1/5) and (1/3, 6/5)

129

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (3√3, √5) and (−√3, 4√5)

135

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, -√2) and (√7,0)

127

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, −√3) and (√5, 0)

130

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (3.5, 8.2) and (-0.5, 6.2)

135

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-2, -6) and (3, −4)

156

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, 0) and (3,-4)

121

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (4, -1) and (-6, 3)

122

views

Textbook Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (2, 3) and (14, 8)

116

views

Textbook Question

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (-2, -8) and (−6, −2)

120

views

Textbook Question

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (6, 8) and (2, 4)

135

views

Textbook Question

Exercises 103–105 will help you prepare for the material covered in the next section. Solve by completing the square: y² – 6y — 4 = 0.

135

views

Textbook Question

Exercises 103–105 will help you prepare for the material covered in the next section. Use a rectangular coordinate system to graph the circle with center (1, -1) and radius 1.

137

views

Textbook Question

Exercises 103–105 will help you prepare for the material covered in the next section. Let (x1, y₁) = (7, 2) and (x2, y2) = (1, −1). Find √[(x2 − x1)² + (y2 − y₁)²]. Express the - answer in simplified radical form.

121

views

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The circle with center (3, 6) and radius 4 has equation _________.

views

Textbook Question

In Exercises 109–111, give the center and radius of each circle. x^2 + y^2 - 4x + 2y - 4 = 0

views

Textbook Question

In Exercises 107–108, write the standard form of the equation of the circle with the given center and radius. Center (-2. 4), r = 6

190

views

Textbook Question

In Exercises 105–106, find the midpoint of each line segment with the given endpoints. (2, 6) and (-12, 4)

174

views

Textbook Question

Find the given distances between points P, Q, R, and S on a number line, with coordi-nates -4, -1, 8, and 12, respectively. d(P, Q)

112

views

Textbook Question

Find the given distances between points P, Q, R, and S on a number line, with coordi-nates -4, -1, 8, and 12, respectively. d(Q,R)

112

views

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The circle with equation x^2+y^2=49 has center with coordinates________ and radius equal to__________ .

115

views

Textbook Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (0, 0), radius 6

122

views

Textbook Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (2, 0), radius 6

112

views

Textbook Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (0, 4), radius 4

130

views

Textbook Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (5, -4), radius 7

112

views

Textbook Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (-2, 5), radius 4

views

Textbook Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 1 and 2. center (√2, √2), radius √2

119

views

Textbook Question

Use each graph to determine an equation of the circle in (a) center-radius form and (b) general form.

104

views

Textbook Question

Use each graph to determine an equation of the circle in (a) center-radius form and (b) general form.

views

Textbook Question

Give the center and radius of the circle represented by each equation. See Examples 3 and 4. x^2+y^2+6x+8y+9=0

108

views

Textbook Question

Give the center and radius of the circle represented by each equation. See Examples 3 and 4. x^2+y^2-4x+12y=-4

106

views

Textbook Question

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. See Examples 3–5. x^2+y^2+4x-8y+32=0

105

views

Textbook Question

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. See Examples 3–5. x^2+y^2+4x+14y=-54

views

Textbook Question

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. See Examples 3–5. x^2+y^2+2x-6y+14=0

views

Textbook Question

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. See Examples 3–5. x^2+y^2+4x+4y+8=0

117

views

Textbook Question

Describe the graph of each equation as a circle, a point, or nonexistent. If it is a circle, give the center and radius. If it is a point, give the coordinates. See Examples 3–5. x^2+y^2-2x+12y-12=0

112

views

Textbook Question

Work each of the following. Find the equation of a circle with center at (-4, 3), passing through the point (5, 8).Write it in center-radius form.

125

views

Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. P(3, -1), Q(-4, 5)

122

views

Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. M((-8, 2), N(3, -7)

views

Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. A(-6, 3), B(-6,8)

views

Textbook Question

In Exercises 67–70, graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. x² + y² = 16, x-y = 4

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (-7/2, 3/2) and (-5/2, -11/2)

124

views

Showing 280 of 280 practice