AnswersCR27 ALG 1-1200310-S2-Degele-VOL7006PIntroduction to Modeling with Functions

Introduction to Modeling with Functions — Cumulative exam Answers

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1
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Which describes the range of the parent absolute value function?

A
{y | y is a real number}
B
{y | y is an integer}
C
{y|y > 0}
D
{y|y < 0}
2
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One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

A
mc017-1.jpg
Option A
B
mc017-2.jpg
Option B
C
mc017-3.jpg
Option C
D
mc017-4.jpg
Option D
3

What are the vertical and horizontal asymptotes for the function ?

Question illustration
A
vertical asymptote: x = 1horizontal asymptote: none
B
vertical asymptote: x = 1horizontal asymptote: y = 0
C
vertical asymptote: x = –2, x = 3horizontal asymptote: y = 0
D
vertical asymptote: x = –2, x = –3horizontal asymptote: none
4

Vladimir rolls a six-sided number cube 36 times. If getting a 3 is a success, what is the probability of a success?

A
One-sixth
Option A
B
One-third
Option B
C
Two-thirds
Option C
D
Five-sixths
Option D
5

Which graph shows the solution to the equation below?

Question illustration
A
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = 1.
Option A
B
On a coordinate plane, a curves starts in quadrant 4 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = negative 1.
Option B
C
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 1. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = 1.
Option C
D
On a coordinate plane, a curves starts in quadrant 3 and curves up into quadrant 1 and approaches y = 2. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = negative 1.
Option D
6

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

A
1.7 years
B
2.0 years
C
3.1 years
D
5.0 years
7

Tyna simplified the expression to . What was Tyna’s mistake?

Question illustration
S
She divided the coefficients incorrectly.
S
She added the exponents instead of subtracting them.
S
She divided the coefficients instead of subtracting them.
S
She subtracted the exponents instead of dividing them.
8

A utility company hires pollsters to knock on random doors in different parts of town to survey residents about the cost of their electric bill. Would this study be biased? Why or why not?

A
No, it is not biased. All residents of the town will have the opportunity to respond.
B
Yes, it is biased. Some of the residents who are surveyed may not want to respond to someone who knocks at their door.
C
No, it is not biased. All residents who are surveyed will want to respond.
D
Yes, it is biased. Only certain parts of the town were surveyed.
9

What is the solution of ?

Question illustration
A
6
B
9
C
18
D
81
10

For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?

Question illustration
a
a = –1, m = 0
a
a = 1, m = 0
a
a = –1, m = 1
a
a = 1, m = 1
11

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
12

What are the solutions to

Question illustration
A
x = negative 2 and x = negative 4
Option A
B
x = negative 1 and x = 8
Option B
C
x = 1 and x = negative 8
Option C
D
x = 2 and x = 4
Option D
13

Johnni guessed on all 8 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that she got exactly 3 questions correct? Round the answer to the nearest thousandth.

Question illustration
A
0.004
B
0.208
C
0.422
D
0.792
14

A graph with both axes numbered 1 to 10. A line increases from 1 to 3 then decreases from 3 to 5.

Question illustration
A
f(x) = 2(x – 5)(x – 1)
B
f(x) = –2(x – 5)(x – 1)
C
f(x) = 2(x + 5)(x + 1)
D
f(x) = –2(x + 5)(x + 1)
15

The number of bacteria in a sample after x days is represented using the equation . By what approximate percent does the population change per day?

Question illustration
A
4.8% decrease
B
5.0% increase
C
95.2% decrease
D
105.0% increase
16

If , what is the value of x?

Question illustration
A
–3
B
–2
C
2
D
3
17

For the inverse variation equation xy = k, what is the constant of variation, k, when x = –2 and y = 5?

A
–10
B
Negative two-fifths
Option B
C
Five-halves
Option C
D
10
18

How many 2-letter combinations can be created from the distinct letters in the word “mathematician”? Assume that the order of the letters does not matter.

A
28
B
56
C
78
D
156
19

Veronique has a spinner with three sections of equal size, red (r), green (g), and blue (b).The spinner is spun twice. The sample space for the possible outcomes is S = {rr, rb, rg, gr, gg, gb, br, bg, bb}. If the number of times red is spun is the random variable, X, which graph represents the probability distribution?

A
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.43; 1 time is 0.43; 2 times is 0.1.
Option A
B
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.33; 1 time is 0.33; 2 times is 0.33.
Option B
C
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.55; 1 time is 0.32; 2 times is 0.11.
Option C
D
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.5; 1 time is 0.38; 2 times is 0.12.
Option D
20

Mrs. Cho wrote the following problem on the board.Problem: Step 1: Step 2: Step 3: What should Mrs. Cho do next?

Question illustration
A
Find a common denominator for the two fractions.
B
Divide the numerator and denominator of the first fraction by x2 and y.
C
Multiply the numerators, multiply the denominators, and then simplify.
D
Multiply the first fraction by the reciprocal of the second fraction.

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