Deck 3: Functions and Their Graphs

Question 1

Write an equation that describes the variation. Use k as the constant of variation.
V is directly proportional to .

Answer 1

Question 2

Write an equation that describes the variation. Use k as the constant of variation.
A varies directly with both and .

Answer 2

Question 3

Write an equation that describes the variation. Use k as the constant of variation.
f varies inversely with both and .

Answer 3

Question 4

Write an equation that describes the variation.
s varies directly with the cube of T. s = 84,375 when T = 15.

Question 5

Write an equation that describes the variation.
V varies directly with m and inversely with q. V = 130 when m = 35 and q = 25.

Question 6

Write an equation that describes the variation.
s varies inversely with both x and the square root of q. s = 47 when x = 18 and q = 1.

Question 7

Write an equation that describes the variation.
z varies directly with the square root of x and inversely with the cube of u. when and

Question 8

Write an equation that describes the variation. P varies directly with the square root of x and inversely with the cube of u. when and

A)
B)
C)
D)

Question 9

A force of 102 N will stretch the spring 17 cm. How far will a force of 120 N stretch the spring?

Question 10

A gas contained in a 30 mL container at a temperature of 200 K has a pressure of 1,600 atm. If the temperature increases to 210 K, what is the resulting pressure?

Question 11

Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kx
where F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).
A force of 300 N will stretch the spring 20 cm. How much force is required to stretch the spring

Question 12

A gas contained in a 2 mL container at a temperature of 320 K has a pressure of 1.5 atm. If the container changes to a volume of 1 mL, what is the resulting pressure?

Question 13

Levi's makes jeans in a variety of price ranges for juniors. The Silver Tab Baggy jeans sell for about $37, whereas the Offender jeans sell for $150. The demand for Levi's jeans is inversely proportional to the price. If 235,000 pairs of the Silver Tab Baggy jeans were bought, approximately how many of the Offender were bought? Round to the nearest integer.

Question 14

In physics, the inverse square law states that any physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. In particular, the intensity of light radiating from a point source is inversely proportional to the square of the distance from the source. Below is a table of average distances from the Sun:

The solar radiation on the Earth is approximately 1,250 watts per square meter. How much solar radiation is there on Mercury? Round to the nearest hundredth watts per square meter.

Question 15

Write an equation that describes the variation. Use k as the constant of variation.
V is directly proportional to .

A)
B)
C)
D)

Question 16

Write an equation that describes the variation. Use k as the constant of variation.
V varies directly with the cube of z.

A)
B)
C)
D)

Question 17

Write an equation that describes the variation. Use k as the constant of variation.
F is inversely proportional to .

A)
B)
C)
D)

Question 18

Write an equation that describes the variation. Use k as the constant of variation.
P varies inversely with the square of h.

A)
B)
C)
D)

Question 19

Write an equation that describes the variation. Use k as the constant of variation.
P is directly proportional to both and .

A)
B)
C)
D)

Question 20

Write an equation that describes the variation. Use k as the constant of variation.
P is inversely proportional to both and .

A)
B)
C)
D)

Question 21

Write an equation that describes the variation.
A is directly proportional to the cube of L. A = 2 when L = 1.

A)
B)
C)
D)

Question 22

Write an equation that describes the variation.
F is inversely proportional to the square of t. f = 8 when t = 1.

A)
B)
C)
D)

Question 23

Write an equation that describes the variation. Use k as the constant of variation.
V varies is directly proportional to both and . V = 32 when x = 1 and t = 4.

A)
B)
C)
D)

Question 24

Write an equation that describes the variation.
F is inversely proportional to both ? and L. F = when ? = 7?m and L = 200 km.

A)
B)
C)
D)

Question 25

Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kx
Where F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).A force of 352 N will stretch the spring 22 cm. How far will a force of 288 stretch the spring? Round to two decimal places.

A) 0.27 m
B) 26.89 m
C) 0.18 m
D) 18.00 m

Question 26

Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kxwhere
F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).A force of 429 N will stretch the spring 33 cm. How much force to the nearest Newtons is required to stretch the spring 72 cm?

A) 196.63 N
B) 936.00 N
C) 1,019,304.00 N
D) 9.36 N

Question 27

In physics, the inverse square law states that any physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. In particular, the intensity of light radiating from a point source is inversely proportional to the square of the distance from the source. Below is a table of average distances from the Sun:

The solar radiation on the Earth is approximately 1560 watts per square meter. How much solar radiation is there on Mercury? Round to the nearest hundred watts per square meter.

A) 605,172,413.79 watts per square meter
B) 4034.48 watts per square meter
C) 10,434.01 watts per square meter
D) 0.07 watts per square meter

Question 28

A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1.5 atm. If the temperature decreases to 325 K, what is the resulting pressure?

A) 165,750.0 atm
B) 1.6 atm
C) 170.0 atm
D) 1.4 atm

Question 29

A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1 atm. If the container changes to a volume of 2 mL, what is the resulting pressure?

A) 113.3 atm
B) 0.7 atm
C) 1.5 atm
D) 6.0 atm

Question 30

Levi's makes jeans in a variety of price ranges for juniors. The Flare 519 jeans sell for about $19, whereas the 646 Vintage Flare jeans sell for $150. The demand for Levi's jeans is inversely proportional to the price. If 200,000 pairs of the Flare 519 jeans were bought, approximately how many of the 646 Vintage Flare were bought? Round to the nearest integer.

A) 1,578,947 pairs of the 646 Vintage Flare
B) 25,333 pairs of the 646 Vintage Flare
C) 1333 pairs of the 646 Vintage Flare
D) 10,526 pairs of the 646 Vintage Flare

Question 31

Determine if the relationship f = {(18, 12), (2, 1), (-8, 1), (-20, -3)} is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 32

Determine if the relationship f = {(9, -3), (-17, 12), (5, -6), (-15, -18)} is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 33

Determine if the relationship f = {(-1, 6), (-1, -7), (15, -7), (5, 3)} is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 34

Determine if the relationship y = is a function. If it is a function, determine if it is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 35

Determine if the relationship x = + 20 is a function. If it is a function, determine if it is a one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 36

Determine if the relationship y = -9 is a function. If it is a function, determine if it is one-to-one function.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 37

Determine if the relationship y = , x > 0 is a function. If it is a function, determine if it is one-to-one.

A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Question 38

The function y = 9 - 2x is a one-to-one function. Find its inverse.

A)
B)
C)
D)

Question 39

The function f (x) = + 3, x ? 0 is a one-to-one function. Find its inverse.

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

Question 40

The function f (x) = + 8, x ? 3 is a one-to-one function. Find its inverse.

A)
B)
C)
D)

Question 41

The function f (x) = , x ? is a one-to-one function. Find its inverse.

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

Question 42

The function f (x) = x > 7, is a one-to-one function. Find its inverse.

A) y =
B) y = 7
C) y =
D) y =

Question 43

The function f (x) = , x > -8 is a one-to-one function. Find its inverse.

A) y =
B) y = -8
C) y = -
D) y =

Question 44

Determine if the relationship y = , x > 0 is a function. If it is, determine if it is a one-to-one function.

Question 45

The function f (x) = , x ≥ is a one-to-one function. Find its inverse.

Question 46

Determine whether the function is a one-to-one function.

Question 47

Determine whether the function is a one-to-one function.

A) not a one-to-one function
B) a one-to-one function

Question 48

Given the graph of a one-to-one function: plot its inverse.

Question 49

Given the graph of a one-to-one function: plot its inverse.

A)

B)

C)

D)

Question 50

Given the graph of a one-to-one function: plot its inverse.

Question 51

Given the graph of a one-to-one function: plot its inverse.

A)

B)

C)

D)

Question 52

A student work at Target making $12.90 per hour and the weekly number of hours worked per week, x, varies. If Target withholds 16% of his earnings for taxes and Social Security, write a function, E(x), that expresses the student's take-home pay each week. Find the inverse function, (x). What does the inverse function tell you?

Question 53

The function f (x) = , x ? is a one-to-one function. Verify that y = is its inverse.

A) The function is not the inverse of f (x)
B) The function is the inverse of f (x)
C) The function f (x) does not have an inverse

Question 54

The function f (x) = + 6, x ? 1 is a one-to-one function. Verify that + 5 is its inverse.

A) The function is not the inverse of f (x)
B) The function is the inverse of f (x)
C) The function f (x) does not have an inverse

Question 55

The relationship, f (x) = , is a function. Determine if it is a one-to-one function.

Question 56

Given the functions f (x) = 3x + 6 and g(x) = -6x + 8, find (f + g)(x).

A) -3x + 14
B) -3x + 2
C) 9x + 14
D) -18x + 48

Question 57

Given the functions find (f + g)(x).

A)
B)
C)
D)

Question 58

Given the functions ,find (f + g)(x).

A)
B)
C)
D)

Question 59

Given the functions f (x) = 18 - 4x and g(x) = 3x + 2, find (f - g)(x).

A) -7x + 16
B) -7x - 16
C) -7x + 20
D) 7x + 20

Question 60

Given the functions ,find (f - g)(x).

A)
B)
C)
D)

Question 61

Given the functions f (x) = x + 3 and g(x) = 6x - 9, find (f · g)(x).

A)
B)
C)
D)

Question 62

Given the equations ,find (f ? g)(x).

A)
B)
C)
D)

Question 63

Given the functions f (x) = 24x + 24 and g(x) = 6x + 6, find (x). (Assume g(x) ? 0.)

A) 144 + 144x + 144
B) 1/4
C) 4
D) 30x + 30

Question 64

Given the functions f (x) = - 9 and g(x) = x - 3, find (x). (Assume g(x) ? 0.)

A) x + 3
B) x - 9
C) - x - 6
D) x + 9

Question 65

Given the equations f (x) = 2x + 6 and g(x) = 3x - 10, find (f ? g)(x).

A) 5x - 4
B) 6x - 20
C) 6x - 14
D) 6x + 20

Question 66

Given the functions f (x) = and g(x) = , find (f ? g)(x).

A)
B)
C)
D)

Question 67

Given the functions f (x) = 8x + 1 and g(x) = 3x - 7, find (g ? f)(x).

A) 24x - 7
B) 24x - 6
C) 24x + 31
D) 24x - 4

Question 68

Given the functions f (x) = and g(x) = 7 - x, find (g ? f)(x).

A)
B) 7 -
C)
D)

Question 69

Given the functions f (x) = 3 - 1 and g(x) = 5 - 2x, find find (f ? g)(5).

A) 74
B) [$n]
C) -30 - 25
D) 674

Question 70

Given the function ,find (f ? g)

A)
B)
C)
D)

Question 71

Given the functions f (x) = 8x - 9 and g(x) = 3x + 5, determine f + g, f - g, fg, and .

Question 72

Given the functions f (x) = and g(x) = + 10, determine the composite functions and

Question 73

Given the functions f (x) = 8 - 10x, and g(x) = -4 - x, find and

Question 74

Typical supply and demand relationships state that as the number of units for sale increases, the market price decreases. Assume that the market price, p, and the number of units for sale, x, are related by the demand equation:
p = 1,600 - x
Assume that the cost, C(x), of producing x items is governed by the equation
C(x) = 1,000 + 70x
and the revenue, R(x), generated by selling x units is governed by
R(x) = 400x
a. Write the cost as a function of price p.
b. Write the revenue as a function of price p.
c. Write the profit as a function of price p.

Question 75

Given the functions f (x) = -7 + 8x - 7, and g(x) = 12 - 4x, find and .

Question 76

Given the functions , find

A)

B)
C)

D)

Question 77

Given the functions f (x) = 8x - 1 and g(x) = 4x + 5, determine .

Question 78

Given the function (f ? g) ,choose the two f and g that could make the composite.

A)
B)
C)
D)

Question 79

The graph of y = shifted down 5 and to the right 14. Write the resulting function.

A)
B)
C)
D)

Question 80

The graph of y = shifted up 1 and to the left 20. Write the resulting function.

A)
B)
C)
D)