AnswersS1S-OC Pre-Calculus A E3700 - AGPerformance Task: Modeling with Sinusoidal Functions

Performance Task: Modeling with Sinusoidal Functions — Cumulative exam Answers

25 verified answers
1
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What is the product?

Question illustration
A
StartFraction k + 1 Over k squared EndFraction
Option A
B
StartFraction k minus 1 Over k squared EndFraction
Option B
C
StartFraction negative 1 Over k EndFraction
Option C
D
StartFraction 1 Over k EndFraction
Option D
2
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A cliff diver leaps from a 100-foot cliff into the Pacific. The diver’s height above the water is modeled by the functionP(x) = –16x 2 + 10x + 100, where x is time in seconds.During which interval is the diver at least halfway down?

A
2.0 < x < 2.1 seconds
B
2.1 < x < 2.8 seconds
C
3.0 < x < 3.4 seconds
D
3.4 < x < 3.5 seconds
3

Randy and Trey take turns cleaning offices on the weekends. It takes Randy at most 4 hours to clean the offices. It takes Trey at most 6 hours to clean the offices. What is the greatest amount of time it would take them to clean the offices together?

A
2.4 hours
B
2.5 hours
C
3.0 hours
D
4.0 hours
4

An equation for the depreciation of a car is given by y = A(1 – r)t, where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

A
years
Option A
B
years
Option B
C
3 years
D
4 years
5

Which expression is a possible leading term for the polynomial function graphed below?

Question illustration
A
–18x14
B
–10x7
C
17x12
D
22x9
6

Suppose f(x) = 2(x + 1)2 and f(g(x)) = 2(2x + 4)2. What is g(x)?

A
g(x) = x + 3
B
g(x) = x + 4
C
g(x) = 2x + 3
D
g(x) = 2x + 4
7

Suppose . Which value(s) of a would make the composite functions commutative?

Question illustration
A
0
B
2
C
any value of a
D
no value of a
8

Which property of multiplication is shown below? If x = 3 + 4i and y = 5 + 6i, x × y = y × x.

A
commutative property
B
identity property
C
distributive property
D
associative property
9

Which equation has x = 4 as the solution?

A
log Subscript 4 Baseline (3 x + 4) = 2
Option A
B
log Subscript 3 Baseline (2 x minus 5) = 2
Option B
C
log Subscript x Baseline 64 = 4
Option C
D
log Subscript x Baseline 16 = 4
Option D
10

On which interval are both the sine and cosine functions increasing?

A
(StartFraction 3 pi Over 2 EndFraction, 2 pi)
Option A
B
(StartFraction pi Over 2 EndFraction, pi)
Option B
C
(0, pi)
Option C
D
(pi, StartFraction 3 pi Over 2 EndFraction
Option D
11

Which graph shows the solution set of ?

Question illustration
A
mc017-2.jpg
Option A
B
mc017-3.jpg
Option B
C
mc017-4.jpg
Option C
D
mc017-5.jpg
Option D
12

What is the range of the function f(x) = –2(6x) + 3?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
13

What is the difference quotient of the function g(x) = 4x?

A
; h ≠ 0
B
; h ≠ 0
C
; h ≠ 0
D
; h ≠ 0
14

What is the additive inverse of the expression below, where a and b are real numbers?

Question illustration
A
-1
B
0
C
2 a minus b
Option C
D
Negative 2 a minus b
Option D
15

The average high temperature during the hottest month in Beijing, China, is 72°F. The average high temperature during the coldest month in Beijing is 18°F. The function , where m represents the number of months after January, models the temperature throughout the year in Beijing.During which month in the year would the temperature reach 55°F?

Question illustration
A
August
B
September
C
November
D
December
16

Which statements comparing the graphs of function 1 and function 2 are true? Check all that apply.

A
Function 1 has a hole, while function 2 does not.
B
Function 1 has an oblique asymptote, while function 2 does not.
C
Function 2 has a hole, while function 1 only has asymptotes.
D
Function 2 only has asymptotes, while function 1 has a hole.
E
Both functions have the same domain restriction.
F
Both functions have the same vertical asymptote.
17

The president of a company creates a graph of the price of the company’s stock over one year. He describes the graph as follows:• The price of the stock rose to about $17 before falling to about $3.• There have only been two periods during which the price of the stock decreased.• The price of the stock is expected to increase in the long run.Which graph correctly shows the price of the stock?

A
mc026-1.jpg
Option A
B
mc026-2.jpg
Option B
C
mc026-3.jpg
Option C
D
mc026-4.jpg
Option D
18

What is the solution to x 4 + 4x 3 ≤ 12x 2?

A
(–6, 2)
B
[–6, 2]
C
(–ꝏ, –6) U (2, ꝏ)
D
(–ꝏ, –6] U [2, ꝏ)
19

Review the table showing the population of a city.Years since 2000Population (Thousands of People)211.2312.5513.4615.6722.0924.61225.11626.0

A
a = 27.47, b = 3.26, and c = 0.30
B
a = 27.47, b = 3.26, and c = 0.30
C
a = 3.26, b = 0.30, and c = 27.47
D
a = 3.26, b = 0.30, and c = 27.47
E
a = –0.09, b = 4.53, and c = 2.81
F
a = –0.09, b = 4.53, and c = 2.81
G
a = –0.09, b = 2.81, and c = 4.53
H
a = –0.09, b = 2.81, and c = 4.53
20

What is rewritten using the power property?

Question illustration
A
e log Subscript 6 Baseline f
Option A
B
f log Subscript 6 Baseline e
Option B
C
log Subscript 6 Baseline (e times f)
Option C
D
log Subscript 6 Baseline (e + f)
Option D

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