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)

817

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)

270

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)

287

views

Textbook Question

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

724

views

Textbook Question

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

361

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)

314

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)

256

views

Textbook Question

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

308

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)

253

views

Textbook Question

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

262

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

254

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

291

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

253

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

256

views

Textbook Question

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

285

views

Textbook Question

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

276

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

299

views

Textbook Question

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

318

views

Textbook Question

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

341

views

Textbook Question

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

432

views

Textbook Question

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

290

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

515

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

282

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

281

views

Textbook Question

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

300

views

Textbook Question

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

326

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

275

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)

426

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)

286

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

269

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)

340

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)

360

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)

308

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)

339

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)

319

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

257

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

263

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

271

views

Textbook Question

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

260

views

Textbook Question

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

250

views

Textbook Question

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

253

views

Textbook Question

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

356

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)

314

views

Textbook Question

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

293

views

Textbook Question

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

284

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)])

279

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

613

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

540

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

793

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

348

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

318

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)

359

views

Textbook Question

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

301

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

405

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|

344

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

438

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

975

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)

255

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

796

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)

447

views

Textbook Question

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

281

views

Textbook Question

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

268

views

Textbook Question

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

420

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.

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.

views

Textbook Question

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

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.

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.

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)

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)

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)

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

104

views

Textbook Question

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

views

Textbook Question

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

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)

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)

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)

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 _____.

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 ________ .

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

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)}

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)}

110

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.

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.

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)

164

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)}

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

views

Textbook Question

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

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

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

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

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

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

134

views

Textbook Question

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

views

Textbook Question

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

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

148

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.

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

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^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|

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.

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. x=y^4

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

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

views

Textbook Question

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

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)

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)

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

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?

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?

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?

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?

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?

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

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

views

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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

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

views

Textbook Question

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

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.

views

Textbook Question

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

views

Textbook Question

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

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

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

views

Textbook Question

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

views

Textbook Question

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

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.

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.

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

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

views

Textbook Question

Graph each equation. 2x +5y = 20

views

Textbook Question

Graph each equation. 3y = x

views

Textbook Question

Graph each equation. ƒ(x) = x

views

Textbook Question

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

views

Textbook Question

Graph each equation. x - 4y = 8

views

Textbook Question

Graph each equation. x = -5

views

Textbook Question

Graph each equation. ƒ(x) = 3

views

Textbook Question

Graph each function. ƒ(x) = -|x|

views

Textbook Question

Graph each function. ƒ(x) = |x| -3

views

Textbook Question

Graph each function. ƒ(x) = 2∛(x+1)-2

views

Textbook Question

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

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

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|

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)

140

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.

f(-2)

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.

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.

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.

views

Textbook Question

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

views

Textbook Question

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

102

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)

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)

views

Textbook Question

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

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.

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

views

Textbook Question

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

views

Textbook Question

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

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.

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.

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.

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

129

views

Textbook Question

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

115

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)

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)

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__________ .

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

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

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

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

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

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

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

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

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

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

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

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.

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)

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)

views

Showing 280 of 280 practice

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

3. Functions

Intro to Functions & Their Graphs

Learn with Nick

Practice this topic