Deck 3: Functions and Graphs

Question 1

Find the domain of

A)
B)
C)
D)
E)

Answer 1

Question 2

Find the midpoint of the segment AB between the points A (- 3, - 5) and B (15, 7)

A)( 6, 1 )
B)( 15, 1 )
C)( 3, 1 )
D)( 1, 1 )
E)( 6, 7 )

Answer 2

( 6, 1 )

Question 3

Let y = f (x) be a function with domain D = [ -6, -3 ] and range R = [ -8, -2 ]. Find the domain D and range R for the function

A)
B)
C)
D)
E)

Answer 3

Question 4

A cable television firm presently serves 5,900 households and charges $22 per month. A marketing survey indicates that each decrease of $1 in the monthly charge will result in 590 new customers. Let R(x) denote the total monthly revenue when the monthly charge is x dollars. Find the value of x that results in maximum monthly revenue.

A)$21
B)$6
C)$11
D)$16
E)$22

Question 5

Find the domain of

A)
B)
C)
D)
E)

Question 6

Express the function in the form of .

A)
B)
C)
D)
E)

Question 7

Express the function in the form of

A)
B)
C)
D)
E)

Question 8

The owner of an ice cream franchise must pay the parent company $1,100 per month plus 5% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $2,500 per month for items such as utilities and labor. The cost of ice cream and supplies is 50% of the revenue. Determine the monthly revenue needed to break even.

A)$3,600
B)$1,620
C)$1,400
D)$8,000
E)$6,545

Question 9

If are real numbers, find

A)f ( a ) + f ( h ) = a ² + h ² + a + h + 6
B)f ( a ) + f ( h ) = a ² + h ² - a - h + 6
C)f ( a ) + f ( h ) = a ² + h ² - a - h
D)f ( a ) + f ( h ) = a ² + h ² - a - h - 6
E)f ( a ) + f ( h ) = a ² + h ² + a + h

Question 10

Given the two lines graphed on the same coordinate plane, find the coordinates of the point of intersection (the coordinates are integers).

A)( - 17, 11 )
B)( - 11, 14 )
C)( - 11, 12 )
D)( - 16, 12 )
E)( - 11, 17 )

Question 11

Consider the following equations and their graph. Express, in interval form, the x-values such that Y ₁ > Y ₂ . Assume that the x- and y-values of each point of intersection are integers.

A)
B)
C)
D)
E)

Question 12

Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 9 from P(3, 4).

A)( - 3.90, - 1.95 )
B)( - 4.00, - 1.90 )
C)( - 3.70, - 1.85 )
D)( - 4.00, - 7.99 )
E)( - 3.80, - 1.90 )

Question 13

Use tests for symmetry to determine if the graph of the function is symmetric with respect to the y-axis, the x-axis, or the origin.

A)the graph is symmetric with respect to the x-axis
B)the graph is symmetric with respect to the y-axis
C)the graph is symmetric with respect to the x-axis and the y-axis
D)the graph is symmetric with respect to the origin
E)the graph is not symmetric

Question 14

Find the equation of the circle that satisfies the conditions:

A)(x + 2) ² + (y - 8) ² = 6
B)(x - 2) ² + (y + 8) ² = 36
C)(x - 2) ² + (y + 8) ² = 6
D)(x + 2) ² + (y + 8) ² = 36
E)(x + 2) ² - (y + 8) ² = 36

Question 15

Find the graph of the line through for the value of =

A)
B)
C)
D)
E)

Question 16

Sketch the graphs of the lines on the same coordinate plane.

A)
B)
C)
D)
E)

Question 17

Find the distance d (A, B) between the points A (3, - 2) and B (8, 3).

A)6.77
B)6.07
C)7.07
D)7.57
E)6.97

Question 18

A college student receives an interest-free loan of $8,875 from a relative. The student will repay $155 per month until the loan is paid off. After how many months will the student owe $5,000?

A)after 32 months.
B)after 26 months.
C)after 22 months.
D)after 25 months.
E)after 12.5 months.

Question 19

Sketch the graph of f

A)
B)
C)
D)

Question 20

Given A (7, -3) and B (-9, 9), find the point on segment AB that is three-fourths of the way from A to B.

A)( 3, 0 )
B)( -6, 3 )
C)( -5, 6 )
D)( 6, -5 )
E)( 0, 3 )

Question 21

Use tests for symmetry to determine if the graph of the function is symmetric with respect to the y-axis, the x-axis, or the origin.

A)the graph is symmetric with respect to the x-axis and the y-axis
B)the graph is symmetric with respect to the y-axis
C)the graph is symmetric with respect to the origin
D)the graph is symmetric with respect to the x-axis
E)the graph is not symmetric

Question 22

Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 8 from P(2, 1).

A)( - 5.36, - 2.58 )
B)( - 5.26, - 2.63 )
C)( - 5.06, - 2.53 )
D)( - 5.16, - 2.58 )
E)( - 5.36, - 10.71 )

Question 23

Find the distance d (A, B) between the points A (4, - 6) and B (7, 3).

A)8.49
B)9.49
C)9.19
D)9.39
E)9.99

Question 24

Find the domain of

A)
B)
C)
D)
E)

Question 25

Consider the following equations and their graph. Express, in interval form, the x-values such that Y ₁ > Y ₂ . Assume that the x- and y-values of each point of intersection are integers.

A)
B)
C)
D)
E)

Question 26

Find the domain of

A)
B)
C)
D)
E)

Question 27

Find and

A)
B)
C)
D)
E)

Question 28

An object is projected vertically upward from the top of a building with an initial velocity of ft/sec. Its distance in feet above the ground after seconds is given by the equation Find its maximum distance above the ground.

A) ft
B) ft
C) ft
D) ft
E) ft

Question 29

A college student receives an interest-free loan of $8,250 from a relative. The student will repay $125 per month until the loan is paid off. After how many months will the student owe $5,000?

A)after 2.6 months.
B)after 26 months.
C)after 40 months.
D)after 28 months.
E)after 23 months.

Question 30

Find a composite function form for y if:

A)
B)
C)
D)
E)

Question 31

If are real numbers, find

A)f ( a ) + f ( h ) = a ² + h ² + a + h
B)f ( a ) + f ( h ) = a ² + h ² - a - h
C)f ( a ) + f ( h ) = a ² + h ² + a + h + 2
D)f ( a ) + f ( h ) = a ² + h ² - a - h - 2
E)f ( a ) + f ( h ) = a ² + h ² - a - h + 2

Question 32

Find the equation of the circle that satisfies the conditions:

A)(x - 9) ² + (y + 6) ² = 4
B)(x + 9) ² + (y - 6) ² = 4
C)(x + 9) ² + (y + 6) ² = 16
D)(x - 9) ² + (y + 6) ² = 16
E)(x + 9) ² - (y + 6) ² = 16

Question 33

Find the domain of

A)
B)
C)
D)
E)

Question 34

Given A (2, -1) and B (-6, 7), find the point on segment AB that is three-fourths of the way from A to B.

A)( 1, 0 )
B)( 5, -4 )
C)( 0, 1 )
D)( -4, 5 )
E)( -2, 0 )

Question 35

Sketch the graphs of the lines on the same coordinate plane.

A)
B)
C)
D)
E)

Question 36

The owner of an ice cream franchise must pay the parent company $1,200 per month plus 7% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $2,300 per month for items such as utilities and labor. The cost of ice cream and supplies is 53% of the revenue. Determine the monthly revenue needed to break even.

A)$5,833
B)$8,750
C)$3,500
D)$1,400
E)$1,100

Question 37

Find the graph of the line through for the value of =

A)
B)
C)
D)
E)

Question 38

Find the midpoint of the segment AB between the points A (- 5, - 3) and B (9, 13)

A)( 2, 5 )
B)( 3, 5 )
C)( 5, 5 )
D)( 9, 5 )
E)( 2, 13 )

Question 39

A 100-foot-long cable of diameter 2 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 900in ² per year. Express the diameter d of the cable as a function of time t (in years). (Disregard corrosion at the ends of the cable.)

A) inches
B) inches
C) inches
D) inches
E) inches

Question 40

Given the two lines graphed on the same coordinate plane, find the coordinates of the point of intersection (the coordinates are integers).

A)( - 11, 17 )
B)( - 17, 11 )
C)( - 11, 14 )
D)( - 16, 12 )
E)( - 11, 12 )

Question 41

Let y = f (x) be a function with domain D = [ -10, -6 ] and range R = [ -7, -3 ]. Find the domain D and range R for the function

A)
B)
C)
D)
E)

Question 42

Find the domain of

A)
B)
C)
D)
E)

Question 43

A cable television firm presently serves 6,600 households and charges $20 per month. A marketing survey indicates that each decrease of $1 in the monthly charge will result in 660 new customers. Let R(x) denote the total monthly revenue when the monthly charge is x dollars. Find the value of x that results in maximum monthly revenue.

A)$18
B)$20
C)$15
D)$10
E)$5

Question 44

Find a composite function form for y if:

A)
B)
C)
D)
E)

Question 45

Find the midpoint of the segment AB between the points A (- 1, - 1) and B (13, 9)

A)( 6, 4 )
B)( -1, 4 )
C)( 6, 9 )
D)( 1, 4 )
E)( 13, 4 )

Question 46

Consider the following equations and their graph. Express, in interval form, the x-values such that Y ₁ > Y ₂ . Assume that the x- and y-values of each point of intersection are integers.

A)
B)
C)
D)
E)

Question 47

Given the two lines graphed on the same coordinate plane, find the coordinates of the point of intersection (the coordinates are integers).

A)( - 11, 17 )
B)( - 16, 12 )
C)( - 11, 14 )
D)( - 17, 11 )
E)( - 11, 12 )

Question 48

Sketch the graphs of the lines on the same coordinate plane.

A)
B)
C)
D)
E)

Question 49

An object is projected vertically upward from the top of a building with an initial velocity of ft/sec. Its distance in feet above the ground after seconds is given by the equation Find its maximum distance above the ground.

A) ft
B) ft
C) ft
D) ft
E) ft

Question 50

Express the function in the form of

A)
B)
C)
D)
E)

Question 51

Given A (4, -3) and B (-12, 13), find the point on segment AB that is three-fourths of the way from A to B.

A)( -6, 0 )
B)( -8, 9 )
C)( 0, 1 )
D)( 1, 0 )
E)( 9, -8 )

Question 52

Find the equation of the circle that satisfies the conditions:

A)(x + 6) ² + (y - 4) ² = 4
B)(x - 6) ² + (y + 4) ² = 16
C)(x + 6) ² - (y + 4) ² = 16
D)(x + 6) ² + (y + 4) ² = 16
E)(x - 6) ² + (y + 4) ² = 4

Question 53

A 100-foot-long cable of diameter 2 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 1,000in ² per year. Express the diameter d of the cable as a function of time t (in years). (Disregard corrosion at the ends of the cable.)

A) inches
B) inches
C) inches
D) inches
E) inches

Question 54

Find the distance d (A, B) between the points A (1, - 1) and B (8, 1).

A)7.28
B)6.28
C)6.98
D)7.78
E)7.18

Question 55

Use tests for symmetry to determine if the graph of the function is symmetric with respect to the y-axis, the x-axis, or the origin.

A)the graph is symmetric with respect to the y-axis
B)the graph is symmetric with respect to the origin
C)the graph is symmetric with respect to the x-axis
D)the graph is symmetric with respect to the x-axis and the y-axis
E)the graph is not symmetric

Question 56

Express the function in the form of .

A)
B)
C)
D)
E)

Question 57

Find the point with coordinates of the form (2a, a) that is in the third quadrant and is a distance 7 from P(2, 3).

A)( - 3.35, - 1.68 )
B)( - 3.45, - 1.63 )
C)( - 3.25, - 1.63 )
D)( - 3.15, - 1.58 )
E)( - 3.45, - 6.91 )

Question 58

Sketch the graph of f

A)
B)
C)
D)

Question 59

Find and

A)
B)
C)
D)
E)

Question 60

Find the graph of the line through for the value of =

A)
B)
C)
D)
E)

Question 61

Find the domain of

A)
B)
C)
D)
E)

Question 62

Find the domain of

A)
B)
C)
D)
E)

Question 63

Express the function in the form of .

A)
B)
C)
D)
E)

Question 64

Find a composite function form for y if:

A)
B)
C)
D)
E)

Question 65

Sketch the graph of the equation.

A)
B)
C)
D)
E)

Question 66

Let y = f (x) be a function with domain D = [ -10, -9 ] and range R = [ -10, -7 ]. Find the domain D and range R for the function

A)
B)
C)
D)
E)

Question 67

Find an equation of the line that is tangent to the circle x ² + y ² = 25 at the point P ( 3, 4 ).

A)
B)
C)
D)
E)

Question 68

The owner of an ice cream franchise must pay the parent company $1,100 per month plus 3% of the monthly revenue R. Operating cost of the franchise includes a fixed cost of $2,500 per month for items such as utilities and labor. The cost of ice cream and supplies is 52% of the revenue. Determine the monthly revenue needed to break even.

A)$3,600
B)$8,000
C)$1,620
D)$6,545
E)$1,400

Question 69

A cable television firm presently serves 4,600 households and charges $16 per month. A marketing survey indicates that each decrease of $1 in the monthly charge will result in 460 new customers. Let R(x) denote the total monthly revenue when the monthly charge is x dollars. Find the value of x that results in maximum monthly revenue.

A)$3
B)$9
C)$16
D)$13
E)$15

Question 70

Express the function in the form of

A)
B)
C)
D)
E)

Question 71

Sketch the graph of f

A)
B)
C)
D)

Question 72

If are real numbers, find

A)f ( a ) + f ( h ) = a ² + h ² + a + h + 2
B)f ( a ) + f ( h ) = a ² + h ² - a - h
C)f ( a ) + f ( h ) = a ² + h ² - a - h + 2
D)f ( a ) + f ( h ) = a ² + h ² - a - h - 2
E)f ( a ) + f ( h ) = a ² + h ² + a + h

Question 73

Find and

A)
B)
C)
D)
E)

Question 74

Find the distance d (A, B) between the points A (4, - 7) and B (7, 6).

A)13.24
B)12.34
C)13.84
D)13.34
E)13.04

Question 75

A college student receives an interest-free loan of $8,570 from a relative. The student will repay $170 per month until the loan is paid off. After how many months will the student owe $5,000?

A)after 4.2 months.
B)after 21 months.
C)after 31 months.
D)after 29 months.
E)after 24 months.

Question 76

Find the distance d (A, B) between the points A (2, 1) and B (2, - 3).

A)3
B)1
C)4
D)0

Question 77

Find a formula that expresses the fact that P(x, y) is a distance 4 away from the origin.

A)
B)
C)
D)
E)

Question 78

Find the domain of

A)
B)
C)
D)
E)

Question 79

A 100-foot-long cable of diameter 2 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 500in ² per year. Express the diameter d of the cable as a function of time t (in years). (Disregard corrosion at the ends of the cable.)

A) inches
B) inches
C) inches
D) inches
E) inches

Question 80

An object is projected vertically upward from the top of a building with an initial velocity of ft/sec. Its distance in feet above the ground after seconds is given by the equation Find its maximum distance above the ground.

A) ft
B) ft
C) ft
D) ft
E) ft