Deck 2: Relations, Functions and Graphs

Question 1

Find the equation of a circle with center (2, -3) and the graph of which contains the point (3, 4), then sketch its graph.

Answer 1

(x - 2)² + (y + 3)² = 50 (Gridlines are spaced one unit apart.)

Question 2

Write the equation in factored form to find the center and radius of the circle. Then sketch the graph. x² + y² + 6x - 8 = 0

A) (x + 3)² + y² = 16

(Gridlines are spaced one unit apart.)
B) (x + 3)² + y² = 17

(Gridlines are spaced one unit apart.)
C) (x - 3)² + y² = 16

(Gridlines are spaced one unit apart.)
D) (x - 3)² + y² = 17

(Gridlines are spaced one unit apart.)

Answer 2

(x + 3)² + y² = 17

(Gridlines are spaced one unit apart.)

Question 3

Use the distance formula to find the length of the line segment. (Gridlines are spaced one unit apart.)

A) 7
B)
C)
D)

Answer 3

Question 4

Find the equation of a circle whose diameter has endpoints (2, -7) and (2, 1), then sketch its graph.

Question 5

Determine whether the mapping represents a function or nonfunction. If a nonfunction, explain how the definition of a function is violated.

A) Function.
B) Not a function. Amy is paired with two parents.
C) Not a function. Two children are paired with Bob.
D) Not a function. Some parents are paired with only one child.

Question 6

Determine whether the relation represents a function or a nonfunction. If the relation is a nonfunction, explain how the definition of a function is violated. {(2, -5), (-1, -4), (4, -7), (1, -2), (-1, -6), (6, -8)}

A) Function
B) Not a function; -1 is paired with -4 and -6.

Question 7

Find the equation of a circle with center (-7, 6) and radius .

A) (x + 7)² + (y - 6)² =
B) (x - 7)² + (y + 6)² =
C) (x + 7)² + (y - 6)² = 5
D) (x - 7)² + (y + 6)² = 5

Question 8

Find the midpoint of the segment with endpoints (5, 7) and (3, -5).

A) (8, 2)
B) (2, 12)
C) (4, 1)
D) (1, 6)

Question 9

Complete the table using the given equation. Use these points to graph the relation.

Question 10

Find the equation of a circle with center (0, 0) and radius 10.

Question 11

Identify the center and radius of the circle, then graph. Also, state the domain and range of the relation.
(x - 2)² + (y - 1)² = 9

Question 12

Identify the center and radius of the circle.
x² + (y - 8)² = 4.

Question 13

Identify the center and radius of the circle. (x + 6)² + (y - 4)² = 16.

A) center (-6, 4) and radius 4
B) center (6, -4) and radius 4
C) center (-6, 4) and radius 16
D) center (6, -4) and radius 16

Question 14

Find the equation of a circle with center (-1, 2) and radius . Then sketch its graph.

Question 15

Complete the table using the given equation. If an x input corresponds to two possible y outputs, be sure to find both.
|y - 3| = x

Question 16

Find the equation of a circle with center (0, 0) and radius 4. Then sketch its graph.

Question 17

Find the equation of a circle with center (0, 2) and radius . Then sketch its graph.

A) x² + (y - 2)² =

(Gridlines are spaced one unit apart.)
B) x² + (y - 2)² = 6

(Gridlines are spaced one unit apart.)
C) x² + (y - 2)² =

(Gridlines are spaced one unit apart.)
D) x² + (y - 2)² = 6

(Gridlines are spaced one unit apart.)

Question 18

Determine whether the relation represents a function or a nonfunction. If the relation is a nonfunction, explain how the definition of a function is violated. {(-9, 10), (-12, 11), (-7, 8), (-10, 13), (-13, 11), (-5, 7)}

A) Function
B) Nonfunction; -12 and -13 are both paired with 11.

Question 19

Write the equation in factored form to find the center and radius of the circle.
x² + y² + 14x - 2y + 3 = 0

Question 20

State the domain and range of the relation.
{(5, 8), (6, 9), (7, 10), (8, 11)}

Question 21

Use the following to answer questions :
A car rental company charges a flat fee of $21.50 and an hourly charge of $14.50. This means that cost is a function of the hours the car is rented plus the flat fee.
Write this relationship in equation form.

Question 22

Determine the value of f(18) if f(x) = - x + 1.

Question 23

Determine the value of g(2a) if g(x) = 4x + 1.

Question 24

Use the following to answer questions :
A car rental company charges a flat fee of $21.50 and an hourly charge of $14.50. This means that cost is a function of the hours the car is rented plus the flat fee.
Find the cost if the car is rented for 5.5 hr.

A) $41.50
B) $101.25
C) $36.00
D) $132.75

Question 25

Determine the value of f(-6) if f(x) = -x² - 4x.

A) 30
B) -12
C) 36
D) -40

Question 26

Use the following to answer questions :
h(x) =
Determine the value of .

A) -3
B)
C)
D)

Question 27

Use the following to answer questions :
h(x) =
Determine the value of h(a - 2).

Question 28

Determine whether the relation represents a function or nonfunction, then determine the domain and range of the relation. (Gridlines are spaced one unit apart.)

Question 29

Use the following to answer questions :
h(x) =
Determine the value of h(4).

Question 30

Determine the value of f(a + 1) if f(x) = -5x + 1, then simplify as much as possible.

A) -5a - 4
B) -5a + 2
C) a - 3
D) a - 4

Question 31

Determine the domain of the function.

Question 32

Determine whether the relation represents a function or nonfunction. If a nonfunction, explain how the definition of a function is violated. (Gridlines are spaced one unit apart.)

Question 33

Determine whether the relation represents a function or nonfunction, then determine the domain and range. (Gridlines are spaced one unit apart.)

A) Function


B) Not a function


C) Function


D) Not a function

Question 34

Determine the domain of the function.

A) x $\in$
B) x $\in$
C) x $\in$
D) x $\in$

Question 35

Determine the domain of the function.

Question 36

Determine whether the relation represents a function or nonfunction. If a nonfunction, explain how the definition of a function is violated. (Gridlines are spaced one unit apart.)

A) Function
B) Not a function; 5 and -5 are paired with 0.
C) Not a function; 0 is paired with 3 and -3.
D) Not a function; 6 is not paired with anything.

Question 37

Use the following to answer questions :
A car rental company charges a flat fee of $21.50 and an hourly charge of $14.50. This means that cost is a function of the hours the car is rented plus the flat fee.

-Determine the domain and range of the function in this context, if your budget limits you to paying a maximum of $210 for the rental.

Question 38

Use the following to answer questions :
h(x) =
Determine the value of h(4a).

A) a
B)
C) 16a
D)

Question 39

Use the following to answer questions :
A car rental company charges a flat fee of $21.50 and an hourly charge of $14.50. This means that cost is a function of the hours the car is rented plus the flat fee.
Determine how long the car was rented if the bill came to $152.00.

A) 9 hours
B) 10 hours
C) 11 hours
D) 12 hours

Question 40

Graph using the intercept method.
2x + y = 4

Question 41

Graph by plotting points or using the intercept method.
y = -1

Question 42

Write the equation in function form and identify the new coefficient of x and the new constant term.
5y + 6x = -40

Question 43

Graph by plotting points or using the intercept method. Choose inputs that will help simplify the calculation.
3x + 5y = -6

Question 44

Two points on L₁ and two points on L₂ are given. Use the slope formula to determine if lines L₁ and L₂ are parallel, perpendicular, or neither. L_1: (9, 2) and (3, -8)
L_2: (5, 5) and (-5, -1)

A) Parallel
B) Perpendicular
C) Neither

Question 45

Two points on L₁ and two points on L₂ are given. Use the slope formula to determine if lines L₁ and L₂ are parallel, perpendicular, or neither. L_1: (2, 0) and (6, 2)
L_2: (6, -5) and (8, -9)

A) Parallel
B) Perpendicular
C) Neither

Question 46

Compute the slope of the line through the points (4, 4) and (-4, -7).

A)
B)
C)
D)

Question 47

Two points on L₁ and two points on L₂ are given. Use the slope formula to determine if lines L₁ and L₂ are parallel, perpendicular, or neither. L_1: (3, 4) and (7, 11)
L_2: (9, -9) and (5, -16)

A) Parallel
B) Perpendicular
C) Neither

Question 48

Evaluate the function by selecting three inputs that will result in integer values. Then graph the line.

Question 49

Graph by plotting points or using the intercept method.
y - 3x = 0

Question 50

Graph by plotting points or using the intercept method. x = 3

A)

(Gridlines are spaced one unit apart.)
B)

(Gridlines are spaced one unit apart.)
C)

(Gridlines are spaced one unit apart.)
D)

(Gridlines are spaced one unit apart.)

Question 51

Graph by plotting points or using the intercept method.
x = -2

Question 52

Graph by plotting points or using the intercept method. Plot at least three points. Choose inputs that will help simplify the calculation.

Question 53

Use the following to answer questions :
A business purchases a copier for $9500 and anticipates it will depreciate in value $850 per year.
How many years will it take for the copier's value to decrease to $4350?

Question 54

Use the following to answer questions :
A business purchases a copier for $9500 and anticipates it will depreciate in value $850 per year.
What is the copier's value after 2 years of use?

A) $5150
B) $5200
C) $5250
D) $5300

Question 55

Compute the slope of the line through the points (-5, -1) and (-1, -5).

Question 56

Graph by plotting points or using the intercept method. 3x + 2y = 6

A)
(Gridlines are spaced one unit apart.)
B)
(Gridlines are spaced one unit apart.)
C)
(Gridlines are spaced one unit apart.)
D)
(Gridlines are spaced one unit apart.)

Question 57

Graph using the intercept method.
x + 3y = 6

Question 58

Graph by plotting points or using the intercept method.
y = 4

Question 59

Compute the slope of the line through the points (6, 17) and (1, 7).

Question 60

Two points on L₁ and two points on L₂ are given. Use the slope formula to determine if lines L₁ and L₂ are parallel, perpendicular, or neither. L_1: (-4, -7) and (1, 3)
L_2: (2, 6) and (5, 12)

A) Parallel
B) Perpendicular
C) Neither

Question 61

Graph the linear equation using the y-intercept and the slope indicated.
y = 4x - 5

Question 62

Find the equation of the line in point-slope form, then write the equation in function form.
m = 2; P₁ = (-7, -9)

Question 63

Use the following to answer questions :
4x - 10y = 20
Write the equation in the slope-intercept form.

A)
B)
C)
D)

Question 64

Write the lines in slope-intercept form and state whether they are parallel, perpendicular, or neither. -8x + 6y = -1
4x + 3y = 11

A) Parallel
B) Perpendicular
C) Neither

Question 65

Use the following to answer questions :
A driver going down a straight highway is traveling at 70 ft/sec on cruise control when he begins accelerating at a rate of 4.2 ft/sec². The final velocity of the car is given by the function , where V(t) is the velocity at time t.
If the car is traveling at 100 ft/sec, for how long did it accelerate? (Round to the nearest tenth of a second.)

A) 6.9 seconds
B) 7.1 seconds
C) 7.3 seconds
D) 7.5 seconds

Question 66

Graph the linear equation using the y-intercept and the slope indicated.

A)

B)

C)

D)

Question 67

Use the following to answer questions :
A line has slope m = and passes through the point P₁ = (2, -4).
Write the equation in function form.

A)
B)
C)
D)

Question 68

Use the following to answer questions :
4x - 10y = 20
Identify the slope and y-intercept.

Question 69

Write the equation in slope-intercept form, then identify the slope and y-intercept.
y + 6x = 1

Question 70

Use the following to answer questions :
A line has slope m = and passes through the point P₁ = (2, -4).
Find the equation of the line in point-slope form.

A)
B)
C)
D)

Question 71

Find the equation of the line perpendicular to x - 7y = 28 and through the point (1, -12). Write the answer in slope-intercept form.

Question 72

Use the slope-intercept formula to find the equation of the line with slope 5 and y-intercept (0, 3).

A) y = 3x + 5
B) 3x + 5y = 0
C) y = 5x + 3
D) 5y = 3

Question 73

Use the slope-intercept formula to find the equation of the line with slope with a slope of -4 if the point (4, -9) is on the line.

Question 74

Write the equation in slope-intercept form, then use the slope and intercept to graph the line.
5x + 2y = 6

Question 75

Write the lines in slope-intercept form and state whether they are parallel, perpendicular, or neither. 5y - 3x = 3
3y + 5x = 4

A) Parallel
B) Perpendicular
C) Neither

Question 76

Find the equation of the line which is parallel to -5x + 2y = 12 and through the point (10, 21). Write answer in slope-intercept form.

A) y =
B) y =
C) y =
D) y =

Question 77

Use the following to answer questions :
A driver going down a straight highway is traveling at 70 ft/sec on cruise control when he begins accelerating at a rate of 4.2 ft/sec². The final velocity of the car is given by the function , where V(t) is the velocity at time t.
Interpret the meaning of the slope and y-intercept in this context.

Question 78

Use the following to answer questions :
A driver going down a straight highway is traveling at 70 ft/sec on cruise control when he begins accelerating at a rate of 4.2 ft/sec². The final velocity of the car is given by the function , where V(t) is the velocity at time t.
Determine the velocity of the car after 10.4 seconds.

A) 111.40 ft/sec
B) 112.32 ft/sec
C) 113.68 ft/sec
D) 114.54 ft/sec

Question 79

Write the lines in slope-intercept form and state whether they are parallel, perpendicular, or neither. 7y - 4x = -7
-4x + 7y = 16

A) Parallel
B) Perpendicular
C) Neither

Question 80

Use the following to answer questions :
A line has slope m = and passes through the point P₁ = (2, -4).
Graph the line.