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Composition of Functions and Modeling Answers

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A 2000-kilogram sports car accelerates at a rate of 30 meters per second squared. The velocity of the car is v = at, where a is acceleration in meters per second squared, and t is time in seconds. The kinetic energy of the car is , where m is the mass in kilograms.Which function represents the kinetic energy of the car after accelerating for t seconds?

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A
KE = 1000t2
B
KE = 30,000t2
C
KE = 60,000t2
D
KE = 900,000t2
2
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Anthony sells cars. Each month, he is paid $2,000, plus a 15% commission on monthly sales above $20,000. Which function calculates his monthly earnings (E) as a function of m, his monthly sales?

A
E(m) = 2,000 + 0.15(m – 20,000)
B
E(m) = 2,000 + 0.15(m + 20,000)
C
E(m) = 2,000 + 15(m – 20,000)
D
E(m) = 2,000 + 15(m + 20,000)
3

The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of the completely inflated balloon is 784π cm2, how long will it take for the balloon to fully inflate?Use SA=4πr2.

A
7 seconds
B
10 seconds
C
49 seconds
D
196 seconds
4

Consider the composite function .If f(x) = 3x2, what is g(x)?

Question illustration
A
g (x) = StartRoot 2 x EndRoot
Option A
B
g (x) = StartRoot x + 3 EndRoot
Option B
C
g (x) = StartRoot 6 x EndRoot
Option C
D
g (x) = StartRoot 9 minus x EndRoot
Option D
5

A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet per minute. Approximately how long does it take to inflate the balloon to of its maximum volume? Use π = 3.14 and .

Question illustration
A
16 minutes
B
18 minutes
C
23 minutes
D
26 minutes
6

The Brazilian free-tailed bat can travel 99 miles per hour. After sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. How long before these bats cover an area of 80,000 square miles? Use π = 3.14.

A
0.9 hours
B
1.6 hours
C
2.6 hours
D
5.1 hours
7

Which pair of functions represents a decomposition of f(g(x)) = | 2(x + 1)2 + (x + 1) | ?

A
f(x) = (x + 1)2 and g(x) = | 2x + 1 |
B
f(x) = (x + 1) and g(x) = | 2x2 + x |
C
f(x) = | 2x + 1 | and g(x) = (x + 1)2
D
f(x) = | 2x2 + x | and g(x) = (x + 1)
8

The function represents the composite h(x) = f(g(x)). If f(x) = 2x – 1, what is g(x)?

Question illustration
A
g (x) = two-thirds x
Option A
B
g (x) = two-thirds x minus 1
Option B
C
g (x) = 2 and one-third x
Option C
D
g (x) = 2 and one-third x minus 1
Option D
9

On a coordinate plane, f (x) goes through (negative 5, 6), has a vertex at (0, 1), and goes through (5, 6). G (x) has 2 curves. A curve opens up and to the right in quadrant 1 and approaches the y-axis and x-axis. A curves opens down and to the left in quadrant 3 and approaches the y-axis and x-axis.

Question illustration
A
The graphs of f(x) and g(x) intersect each other.
B
The graph of g(x) contains negative values.
C
The domains of f(x) and g(x) are different.
D
The y-intercepts of f(x) and g(x) are different.
10

Are the compositions of f(x) = 1 and g(x) = 2 commutative? Why or why not?

A
They are commutative, because f(x) and g(x) are constant functions.
B
They are commutative, because f(g(x)) and g(f(x) are constant functions.
C
They are not commutative, because f(x) and g(x) are not equal.
D
They are not commutative, because f(g(x)) and g(f(x) are not equal.

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