Intro to Functions & Their Graphs: Study with Video Lessons, Practice Problems & Examples

For the given functions, f(x) = √(x - 17) and g(x) = √(17 - x)

Find f/g and write the domain.

For the given functions, f(x) = √(x - 17) and g(x) = √(17 - x)

Find fg and write the domain.

For the given functions, f(x) = √(x - 11) and g(x) = √(11 - x)

Find f - g and write the domain.

For the given functions, f(x) = √(x - 11) and g(x) = √(11 - x)

Find f + g and write the domain.

For the given functions, f(x) = √(x + 7) and g(x) = √(x - 13)

Find f/g and write the domain.

For the given functions, f(x) = √(x + 7) and g(x) = √(x - 13)

Find fg and write the domain.

For the given functions, f(x) = √(x - 7) and g(x) = √(x + 1.5)

Find f - g and write the domain.

For the given functions, f(x) = √(x - 7) and g(x) = √(x + 1.5)

Find f + g and write the domain.

For the given functions, f(x) = 27x/(x + 9) and g(x) = 9/(x - 7)

Find f/g and write the domain.

For the given functions, f(x) = 27x/(x + 9) and g(x) = 9/(x - 7)

Find fg and write the domain.

For the given functions, f(x) = 18x/(x + 9) and g(x) = 9/(x - 7)

Find f - g and write the domain.

For the given functions, f(x) = 18x/(x + 9) and g(x) = 9/(x - 7)

Find f + g and write the domain.

For the given functions, f(x) = (9x + 2)/(x² - 49) and g(x) = (8x + 9)/(x² - 49)

Find f/g and write the domain.

For the given functions, f(x) = (9x + 2)/(x² - 49) and g(x) = (8x + 9)/(x² - 49)

Find fg and write the domain.

For the given functions, f(x) = (9x + 2)/(x² - 49) and g(x) = (8x + 9)/(x² - 49)

Find f - g and write the domain.

For the given functions, f(x) = (9x + 2)/(x² - 49) and g(x) = (8x + 9)/(x² - 49)

Find f + g and write the domain.

For the given functions, f(x) = 12 + 3/(2x) and g(x) = 3/(2x)

Find f/g and write the domain.

For the given functions, f(x) = 12 + 3/(2x) and g(x) = 3/(2x)

Find fg and write the domain.

For the given functions, f(x) = 12 + 3/(2x) and g(x) = 3/(2x)

Find f - g and write the domain.

For the given functions, f(x) = 12 + 3/(2x) and g(x) = 3/(2x)

Find f + g and write the domain.

For the given functions, f(x) = √(3x) and g(x) = 6x + 7

Find f/g and write the domain.

For the given functions, f(x) = √(3x) and g(x) = 6x + 7

Find fg and write the domain.

For the given functions, f(x) = √(4x) and g(x) = 8x + 12

Find f - g and write the domain.

For the given functions, f(x) = √4x and g(x) = 8x + 12

Find f + g and write the domain.

For the given functions, f(x) = 12 - 3x² and g(x) = 3x² - 18x + 27

Find f/g and write the domain.

For the given functions, f(x) = 12 - 3x² and g(x) = 3x² - 18x + 27

Find fg and write the domain.

For the given functions, f(x) = 12 - 3x² and g(x) = 3x² - 18x + 27

Find f - g and write the domain.

For the given functions, f(x) = 12 - 3x² and g(x) = 3x² - 18x + 27

Find f + g and write the domain.

For the given functions, f(x) = 5x² + 33x - 14 and g(x) = x + 7

Find f/g and write the domain.

For the given functions, f(x) = 5x² + 33x - 14 and g(x) = x + 7

Find fg and write the domain.

For the given functions, f(x) = 5x² + 33x - 14 and g(x) = x + 7

Find f - g and write the domain.

For the given functions, f(x) = 5x² + 33x - 14 and g(x) = x + 7

Find f + g and write the domain.

For the given functions, f(x) = x - 7 and g(x) = 7x²

Find f/g and write the domain.

For the given functions, f(x) = x - 7 and g(x) = 7x²

Find fg and write the domain.

For the given functions, f(x) = 7x - 1 and g(x) = 7x²

Find f - g and write the domain.

For the given functions, f(x) = 7x - 1 and g(x) = 7x²

Find f + g and write the domain.

For the given functions, f(x) = 5x + 12 and g(x) = x - 6

Find f/g and write the domain.

For the given functions, f(x) = 5x + 12 and g(x) = x - 6

Find fg and write the domain.

For the given functions, f(x) = 4x + 15 and g(x) = x + 6

Find f - g and write the domain.

For the given functions, f(x) = 4x + 15 and g(x) = x + 6

Find f + g and write the domain.

For the given function, find the domain. 

f(x) = (7x + 4)/(x³ + x² - 49x - 49)

For the given function, find the domain. 

f(x) = √(x - 6)/(x - 13)

For the given function, find the domain. 

f(x) = √(x - 11) + √(x + 11)

For the given function, find the domain. 

f(x) = √(69 - 23x)

Consider the three functions f(x) = 3x -8, g(x) = 5x - 4, and h(x) = x² + 2x + 6. Find the value of f(g[h(1)]) without forming the equation for the composite function.

Consider the three functions f(x) = 3x -8, g(x) = 5x - 4, and h(x) = x² + 2x + 6. Find the value of g(f[h(-3)]) without forming the equation for the composite function.

Consider the two functions f(x) = 3x - 8 and g(x) = 5x - 4. Find the value of (f○g)(2) without forming the equation for the composite function.

Solve: fog(x) and also find domain of fog(x) where f(x) = 3x -2; g(x) = √x

Solve: gof(x) and also find domain of gof(x)  where f(x) = x³ -2; g(x) = x² +6x

Solve: gof(x) and also find domain of gof(x) where f(x) = √x +2x; g(x) = x² -2

Solve for g ∘ f(x) and also find the domain of g ∘ f(x).

f(x) = 1/(2-x); g(x) = 2 -1/x

Solve: fog(1/5) where f(x) = x/(x +5); g(x) = 2/x -5

Solve: gof(0) where f(x) = 4x -7; g(x) = (x +7)/4

Solve: (fog) (1) and (gof)(1) where f(x) =  x^1/3; g(x) = x³+2

Solve: gof(x) where f(x) = 4 +√x; g(x) = x² +2x +2

Solve: fog(x) and gof(x) where f(x) = x² -x; g(x) = 4 -x

Solve: fog(x) and gof(x)where f(x) = x +√x; g(x) = x²

Solve: fog(x) where f(x) = 2x +7; g(x) = 5x +1

Solve: fog(x) where f(x) = 5x; g(x) = x +2

Solve the following equation and check: (x + 2)/3 - (x - 4)/2 = 1 - x/8

Determine the values of x that will satisfy the following conditions: f(x) = 3x - 2, g(x) = x² - 5x + 6, and (f o g) (x) = 4

Evaluate the following composite function using the graphs of f and g: (g o f)(2)

Evaluate the following composite function using the graphs of f and g: (f ○ g)(-3)

Graph f - g using the graphs shown.

Find the domain of f/g using the graphs shown.

Find the domain of f + g using the graphs shown.

Find (g/f)(-1) using the graphs of f and g.

Find (fg)(3) using the graphs of f and g.

Find (g - f)(-4) using the graphs of f and g.

Find (f + g)(2) using the graphs of f and g.

For the given function, find the domain. 

f(x) = √(16x + 64)

Determine two functions f and g so that h(x) = (f ○ g)(x): h(x) = 1/(4x - 9)

Determine two functions f and g so that h(x) = (f ○ g)(x): h(x) = |3x - 7|

Determine two functions f and g so that h(x) = (f ○ g)(x): h(x) = ∛(x² + 6)

Determine two functions f and g so that h(x)=(f ○ g)(x): h(x) = (2x + 3)⁵

For the given function, find the domain. 

f(x) = 6/√(4x - 12)

For the given function, find the domain. 

f(x) = √(3x - 12)

For the given function, find the domain. 

f(x) = 16/(8/2x - 2)

For the given function, find the domain. 

f(x) = 9/(x² + 81) - 8/(x² - 81)

For the given function, find the domain. 

f(x) = 4/(x + 8) - 6/(x - 3)

For the given function, find the domain. 

f(x) = 8/(x² - 15x + 26)

For the given function, find the domain. 

f(x) = x² - 15x + 26

For the given function, find the domain. 

f(x) = - 11/(x + 29)

For the given function, find the domain. 

f(x) = 17(x - 13)

The function c is a composition of two functions a and b so that c(x) = ((a ○ b)(x)).

If c(x) = √(x² + 13x - 31), what is a(x) and b(x)?

For the given functions, find (f ◦ g)(x) and the domain of the resulting composite function if f(x) = (2x- 1)(x + 5) and g(x) = 3/x.

For each function, find: the sum, difference, product and quotient of f and g. f(x) = x² - x - 4, g(x) = 2x² + 5

For the given function, find the domain (in interval notation). h(x) = 5x/(x² - x - 30)

For the given function, find the domain (in interval notation). h(x) = 11/(x+6)

In which quadrant does the point (- 11, 17) lie?

"The point (2, y) lies on the graph of the equation y = 7x - 1". What should be the value of y to make this statement true?

In the graph of y = - 9x + 14, solve for the y-intercept.

Is the statement "there are no x-intercepts in the graph of y = 4x² + 9" true? If false, give reasons.

"The midpoint of the line segment formed by joining the points (0, 0) and(13, 13) is 13/2"

Is the statement true? If false, give reasons.

Consider the following points A and B. A(- 4, - 8), B(6, - 2)

If a line segment is to join these two points, calculate the length and midpoint of this line segment.

Consider the following points A and B. A(6, 1), B(2, 7)

If a line segment is to join these two points, calculate the length and midpoint of this line segment.

Identify if the three points given can form a right triangle:

(0,7), (-4,2), (-9,6)

Identify if the three points given can form a right triangle:

(-5,8), (-9,6), (2,7)

Identify if the three points given can form a right triangle:

(-3,-8), (-1,2), (2,17)

Identify if the given set of points are collinear:

(-8,8), (-6,4), (-2,-4)

Identify if the given points are collinear:

(0,12), (-5,-2), (4, -16)

Identify if the given points are collinear:

(-9,10), (-3,8), (2,4)

A line segment has a midpoint at (8,12) and one endpoint at (15,6). Determine the coordinates of the other endpoint.

A line segment has a midpoint at (10,8) and one endpoint at (25,18). Determine the coordinates of the other endpoint.

A line segment has a midpoint at (18c, 18d) and one endpoint at (7c, 9d). Determine the coordinates of the other endpoint.

In the following relation, identify the domain. {(1, 17), (21, 41), (37, 61)}

If the following equation is a function, identify which is the independent variable and which is the dependent variable. k = 13h + 17

A certain function is defined as f(b) = - 5b + 13. Evaluate f(- 7).

Identify whether the following set of ordered pairs is a function or just a mere relation. {(6, 2), (4, 3), (5, 1), (9, 7)}

Identify whether the following set of ordered pairs is a function or just a mere relation. {(1, 6), (3, 4), (5, 9), (6, 7)}

Identify whether the following set of ordered pairs is a function or just a mere relation. {(7, 3), (0, 7), (7, 5)}

Identify whether the following set of ordered pairs is a function or just a mere relation.

Identify if the given set of ordered pairs represents a function. Also, find the domain and range:

{(13,5), (13,-5), (14,14), (15,7), (15,-7)}

Identify if the given set of ordered pairs represents a function. Also, find the domain and range:

{(22,15), (23,17), (23,19), (24,21)}

Identify if the given mapping represents a function. Also, find the domain and range. 

Identify if the given mapping represents a function. Also, find the domain and range. 

Identify if the given table of x and y-values represents a function. Also, find the domain and range. 

Identify if the given graph represents a function. Also, find the domain and range. 

Find out if the given equation represents a function. Also, find the domain and range.
y= -43/(x-35)

Evaluate f(-5) for the function given below.

f(x) = -9x + 17

Evaluate g(-4) for the function given below.

g(x) = -x² + 8x + 3

Evaluate g(8) for the function given below.

g(x) = -x² + 7x + 5

Evaluate f(-8/5) for the function given below. 

f(x) = -10x + 19

Evaluate g(1/2) for the function given below.

g(x) = -x² + 6x + 10

Evaluate g(-1/6) for the function given below.

g(x) = -x² + 36x + 9

Evaluate f(p) for the function given below.

f(x) = -13x + 14

Evaluate g(k) for the function given below.

g(x) = -x² + 9x + 8

Evaluate g(-x) for the function given below.

g(x) = -x² + 19x + 15

Evaluate f(x + 3) for the function given below.

f(x) = -17x + 21

Evaluate f(a + 5) for the function given below.

f(x) = -12x + 23

Evaluate f(4m - 7) for the function given below.

f(x) = -16x + 254

The given set of ordered pairs defines the function f.

f = {(- 3, 9), (0, 11), (5, 13), (8, 8)}

Evaluate f(8) and f(- 3).

For a certain equation, q is a function of p. If this equation in question is 2q + 3p = 16, evaluate q(5).

For a certain equation, q is a function of p. If this equation in question is 2q + 8p² = 6 - 2p, evaluate q(5).

Evaluate the value of the following function for x = 9.

f(x) = [[0.8x]]

Evaluate the value of the following function for x = 3.5.

f(x) = -[[-x]]

Evaluate the value of the following function for x = 5.8.

f(x) = 4 - [[-x]]

Evaluate the value of the following function for x = 11.

f(x) = [[x/6]]

Evaluate the value of the following function for x = 2.

f(x) = [[4 - (x/4)]]

Evaluate the value of the following function for x = -2√3.

f(x) = [[x]]

Consider the following function:

f(x) = -3x³ + 7x

Determine if it is even, odd or neither.

Consider the following function:

f(x) = 6x⁵ - 5x³

Determine if it is even, odd or neither.

Consider the following function:

f(x) = 0.8x⁴ - 9x² + 11

Determine if it is even, odd or neither.

Consider the following function:

f(x) = 5x⁴ - 3x + 15

Determine if it is even, odd or neither.

Consider the following function:

f(x) = (2x + 3)/(5x⁵)

Determine if it is even, odd or neither.

Consider the following function:

f(x) = (7x⁴ + 17)/(6x²)

Determine if it is even, odd or neither.

Identify if the given equation is a function or just a mere relation. x = (1/7)(y²)

Identify if the given equation is a function or just a mere relation. y = ± √(5x + 9)

If f(b) = - 100b² + 20b - 11, evaluate f(- 0.2)

Identify if the graph defined by the following equation is symmetric with respect to the origin, x-axis, y-axis, or none:

8y² + 8x² = 56

Write y = |x - 3| as a piecewise-defined function using the definition of the absolute function.

For the following equation, identify three ordered pairs and show that the graph passes through these points.

7x + 21y = 42

For the following equation, identify three ordered pairs and show that the graph passes through these points.

y = 3x²

For the following equation, identify three ordered pairs and show that the graph passes through these points.

y = |x + 13|

Identify if the given graph represents a function. Also, find the domain and range. 

Identify if the given graph represents a function. Also, find the domain and range. 

Identify if the given graph represents a function. Also, find the domain and range. 

Find out if the given equation represents a function. Also, find the domain and range.
 81x=y⁴/16

Find out if the given equation represents a function. Also, find the domain and range.
3y = -171x +1

Find out if the given relation represents a function. Also, find the domain and range.
8x -3y < 19

Find out if the given equation represents a function. Also, find the domain and range.
y = -77√x

Find out if the given equation represents a function. Also, find the domain and range.
y=√(13-37x)

Find out if the given equation represents a function. Also, find the domain and range.
y = 87/(x -29)

The graph shown has intervals at which it is increasing, decreasing, and at which it is constant. Find the largest open interval of domain at which the shown is increasing. 

The graph shown has intervals at which it is increasing, decreasing, and at which it is constant. Find the largest open interval of domain at which the function is constant. 

Determine the minimum and maximum values of the function shown and the corresponding x-values at which the minimum and maximum are found. 

Determine the minimum and maximum values of the function shown and the corresponding x-values at which the minimum and maximum are found. 

Which of the following is the graph of f(x) = 2x²? Also, find its domain.

Which of the following is the graph of f(x) = (1/2)x³? Also, find its range.

Which of the following is the graph of f(x) = [[(1/2)x]]? What is the value of the function at x = 5.6?

Which of the following is the graph of f(x) = ∛(5x)? Also, determine if an open interval at which the function is decreasing exists.

Which of the following is the graph of f(x) = √(8x)? Also, find its domain.

Using the following graph, write the domain for which the function is continuous. Present the domain in interval notation. 

Using the following graph, write the domain for which the function is continuous. Present the domain in interval notation. 

Using the following graph, write the domain for which the function is continuous. Present the domain in interval notation. 

Using the following graph, write the domain for which the function is continuous. Present the domain in interval notation. 

Graph the following function:

Graph the following function:

Graph the following function:

Graph the following function:

Graph the following function:

Graph the following function:

For the following graph, write its equivalent piecewise function and write its domain and range. 

For the following graph, write its equivalent piecewise function and write its domain and range. 

Evaluate the value of the following function for x = 6.4

where [[.]] is the greatest integer function.

Evaluate the value of the following function for x = 9.4

where [[.]] is the greatest integer function.

Graph the greatest integer function given below. Write the domain and range of the function.

f(x ) = -[[5x]]

Graph the greatest integer function given below. Write the domain and range of the function.

f(x ) = [[4x - 1]]

The cost of x ounces (x > 0) of tea is expressed as f(x) = 45 - 12[[3 - x]] cents. Find the cost of 3.5-ounces of tea.

Identify if the given graph represents a function. Also, find the domain and range. 

Identify if the given graph represents a function. Also, find the domain and range. 

Identify if the given graph represents a function. Also, find the domain and range. 

Identify if the given graph represents a function. Also, find the domain and range. 

Graph the following equation. 6x + 12y = 48

Graph the following equation. 5y = 2x

Graph the following equation. f(x) = 10x

Graph the following equation. 2x - 5y = 30

Graph the following equation. x = - 17

Graph the following equation. f(x) = - 17

Graph the following equation. f(x) = |2x| + 5

Graph the following equation. f(x) = 5∛(x - 8) + 5

Graph the following equation.

Identify if the graph defined by the following equation is symmetric with respect to the origin, x-axis, y-axis, or none:

3y⁵ = x - 7

Identify if the graph defined by the following equation is symmetric with respect to the origin, x-axis, y-axis, or none:

|3x| = |17y|

Draw the graph for the given functions f and g in the same rectangular system and state the relation between both graphs. 

f(x) = (√3)(x), g(x) = (√3)(x) +5

Draw the graphs for the given functions f and g in the same rectangular system and state the relation between both graphs. 

f(x) = -5x, g(x) = -5x -6

Find the value of f(3) using the graph shown below.

Find the x-intercept and the y-intercept of the function using the graph given below.

Find the x-intercept and the y-intercept of the function using the graph given below.

Find the domain and the range of the function using the graph given below.

Without completing the square, determine the given equation.
9x² + 9y² -6x -12y -4 = 0

For the following circle equation, complete the squares in order to write the whole equation in standard form. Identify the center and radius, and then graph.

x² + y² + 7x + 9y + 9/4 = 0

For the following circle equation, complete the squares in order to write the whole equation in standard form. Identify the center and radius, and then graph.

x² + y² - 4x + 18y + 21 = 0

For the following circle equation, complete the squares in order to write the whole equation in standard form. Identify the center and radius, and then graph.

x² + y² - 14y - 15 = 0

For the following circle equation, complete the squares in order to write the whole equation in standard form. Identify the center and radius, and then graph.

x² - 6x + y² - 27 = 0

For the following circle equation, complete the squares in order to write the whole equation in standard form. Identify the center and radius, and then graph.

x² + y² + 6x - 12y + 20 = 0

For the following circle equation, complete the squares in order to write the whole equation in standard form. Identify the center and radius, and then graph.

x² + y² - 4x - 10y - 20 = 0

For the following circle equation, complete the squares in order to write the whole equation in standard form. Identify the center and radius, and then graph.

x² + y² + 4x + 10y + 20 = 0

A circle is described by the equation (x + 5)² + y² = 16.

Graph this circle and identify its center and radius, as well as its domain and range.

A circle is described by the equation x² + (y - 3)² = 16.

Graph this circle and identify its center and radius, as well as its domain and range.

A circle is described by the equation (x + 5)² + (y - 5)² = 9.

Graph this circle and identify its center and radius, as well as its domain and range.

A circle is described by the equation (x + 8)² + (y + 9)² = 81.

Graph this circle and identify its center and radius, as well as its domain and range.

A circle is described by the equation (x - 5)² + (y + 6)² = 169.

Graph this circle and identify its center and radius, as well as its domain and range.

A circle is described by the equation x² + y² = 121.

Graph this circle and identify its center and radius, as well as its domain and range.

For a circle with the following center and radius, find its equation (in standard form).

Center = (- 12, 0), r = 24

For a circle with the following center and radius, find its equation (in standard form).

Center = (- 8, - 16), r = √8

For a circle with the following center and radius, find its equation (in standard form).

Center = (- 15, 18), r = 5

For a circle with the following center and radius, find its equation (in standard form).

Center = (8, 6), r = 3

For a circle with the following center and radius, find its equation (in standard form).

Center = (0, 0), r = 23

For the line segment bounded by the given endpoints, (5√147, - 12) and (23√3, 12), find the midpoint.

For the line segment bounded by the given endpoints, (8√6, - 11) and (2√6, - 13), find the midpoint.

For the line segment bounded by the given endpoints, (10, 11√2) and (−4, 13√2), find the midpoint.

For the line segment bounded by the given endpoints, (- 1, - 2) and (8, - 12), find the midpoint.

A circle with a line segment passing through the center is shown. The endpoints of the line segment lie on the circle. Determine the coordinates of the center and radius of the circle. Also, using those information, what is the standard form of the equation of the circle? 

Find the distance between each pair of points: (-1/3, -4/5) and (2/3, 2/5)

Find the distance between each pair of points: (7/5, 2/7) and (2/5, 9/7)

Find the distance between each pair of points: (5√2, √3) and (-√2, 2√3)

Find the distance between each pair of points: (0, -√5) and (√6, 0)

Find the distance between each pair of points: (0, -√7) and (√3, 0)

Find the distance between each pair of points: (-5.2, 9.1) and (-0.2, 8.1)

Find the distance between each pair of points: (-4, -8) and (5, -7)

Find the distance between each pair of points: (0, 0) and (5, -6)

Find the distance between each pair of points: (6, -3) and (-4, 2)

Find the distance between each pair of points: (1, 6) and (12, 7)

For the line segment bounded by the given endpoints, (- 1, - 9) and (- 5, - 5), find the midpoint.

For the line segment bounded by the given endpoints, (3, 9) and (13, 15), find the midpoint.

Solve the following equation by completing the square: y² - 8y - 3 = 0

On a rectangular coordinate system, graph a circle that has a center at (3,5) and a radius of 2 units.

Given the points (x₁, y₁) = (6, 1) and (x₂, y₂) = (4, -5). Find the distance between the points using the formula √[(x₂ - x₁)² + (y₂ - y₁)²]. Express the answer in simplest form.

The equation of a certain circle is given by x² + y² + 6x - 2y = -6.

Identify the center and radius of the circle.

Consider the following circle with the center at (0, 2) and having a radius of 12.

Write the equation of this circle in standard form.

For the given line segment with the endpoints (4, 0) and (-15, -3), find the midpoint.

Two points on the x-axis M and N, have coordinates of -32 and -11, respectively. Calculate the distance between them.

Two points on the x-axis K and L, have coordinates of -46 and 9, respectively. Calculate the distance between them.

The equation of a certain circle is given by x² + y² = 196.

Identify the center and radius of the circle.

For a circle with the following center and radius, find its equation (in center-radius form) and graph.
Center = (0, 0), r = 19

For a circle with the following center and radius, find its equation (in center-radius form) and graph.
Center = (19, 0), r = 19

For a circle with the following center and radius, find its equation (in center-radius form) and graph.
Center = (0, 19), r = 19

For a circle with the following center and radius, find its equation (in center-radius form) and graph.
Center = (- 11, 13), r = 17

For a circle with the following center and radius, find its equation (in center-radius form) and graph.
Center = (√19, √19), r = √19

For the given circle, write the equation that best describes it and write your answer in standard form and general form.

For the circle described by the following equation, identify the center and radius. x² + y² + 18x + 26y + 150 = 0

For the circle described by the following equation, identify the center and radius. x² + y² - 16x + 26y = - 8

Identify whether the following equation describes a circle or a point, or if it doesn't exist. In the case of a circle, identify its center and radius; for a point, identify the coordinates; otherwise, you don't need to write anything more.

x² + y² + 4x - 12y + 58 = 0

Identify whether the following equation describes a circle or a point, or if it doesn't exist. In the case of a circle, identify its center and radius; a point, identify the coordinates; otherwise you don't need to write anything more. x² + y² + 18x + 18y + 162 = 0

Identify whether the following equation describes a circle or a point, or if it doesn't exist. In the case of a circle, identify its center and radius; a point, identify the coordinates; otherwise you don't need to write anything more. x² + y² - 8x + 34y + 301 = 0

A certain circle has a center at (- 2, 9) and passes through the point (7, 13). Write the equation that best describes this circle in center-radius form.

For the following pair of points, solve for the length of the line segment if it were to join them, and identify the coordinates of its midpoint. H(13, - 5), K(- 17, 11)

Graph the following equations and determine their points of intersection: x² + y² = 25, x - y = 5

Graph the following equations and determine their points of intersection: (x + 1)² + (y - 3)² = 9, y = x + 1

For the line segment bounded by the given endpoints, (- 9/4, 13/4) and (- 23/4, - 21/4), find the midpoint.