A)Select two true equations below.(4 points)

Question

Responses

x4−−√3=x34
cube root of x to the 4th power is equal to x raised to the 3 fourths power

x7−−√=x7
square root of x to the 7th power end root is equal to x to the 7th power

x7−−√3=x73
cube root of x to the 7th power is equal to x raised to the 7 thirds power

x3−−√=x23
square root of x cubed end root is equal to x raised to the 2 thirds power

x−−√=x12
square root of x is equal to x raised to the 1 half power

Question 2
A)Select two expressions that are equivalent to (4x2)3−−−−−√
(4 points)
Responses

64x3
64 x cubed

8x3
8 x cubed

12x6−−−−√
square root of 12 x to the 6th power end root

(4x2)32
open paren 4 x squared close paren raised to the 3 halves power

64x5−−−−√
square root of 64 x to the 5th power end root

Question 3
A)Classify each exponential function as exponential growth or decay by sorting them into the categories below.(4 points)
Exponential Growth Exponential Decay
f(x)=3x

f(x)=12(2.1)x

f(x)=3(0.66)x

f(x)=7(15)x

Question 4
A)What is the x-intercept and y-intercept of f(x)=2(14)x−8
.(4 points)
Responses

x-intercept: (-6,0)

y-intercept: (0, -1)

x-intercept: (-6,0) y-intercept: (0, -1)

x-intercept: none

y-intercept: (0, -6)

x-intercept: none y-intercept: (0, -6)

x-intercept: (-1,0)

y-intercept: (0, -6)

x-intercept: (-1,0) y-intercept: (0, -6)

x-intercept: (-6,0)

y-intercept: (0, -1)

x-intercept: (-6,0) y-intercept: (0, -1)

Question 5
A)What is the vertex of the absolute value function f(x)=2|x+3|−5
?(4 points)
Responses

(3, -5)
(3, -5)

(3, 5)
(3, 5)

(-3, 5)
(-3, 5)

(-3, -5)
(-3, -5)
Question 6
A)
Select the graph below that represents the piecewise function below.

Question 7
A)
Given the two functions below, which one has the greater maximum value?

f(x)=−12(x+3)2−5

(4 points)
Responses

g(x) has the greater maximum value because its maximum is 3 and the maximum of f(x) is -3
g(x) has the greater maximum value because its maximum is 3 and the maximum of f(x) is -3

f(x) has the greater maximum value because its maximum is −12
and the maximum of g(x) is -2
f(x) has the greater maximum value because its maximum is negative 1 half and the maximum of g(x) is -2

f(x) has the greater maximum value because its maximum is 3 and the maximum of g(x) is -3
f(x) has the greater maximum value because its maximum is 3 and the maximum of g(x) is -3

g(x) has the greater maximum value because its maximum is -1 and the maximum of f(x) is -5
g(x) has the greater maximum value because its maximum is -1 and the maximum of f(x) is -5

Question 8
A)Calculate the average rate of change of f(x)=2x−4
over the interval [0, 4].(4 points)
Responses

2
2

154
15 fourths

16
16

4
4
Question 9
A)
Use the table below to answer the next three questions.

The table contains the results of a survey asking people if they have a cat and/or a dog.



What is the probability of selecting a person at random that has a dog?

(4 points)
Responses

296500=0.592
296 over 500 is equal to 0 point 5 9 2

204500=0.408
204 over 500 is equal to 0 point 4 0 8

96500=0.192
96 over 500 is equal to 0 point 1 9 2

200500=0.400
200 over 500 is equal to 0 point 4 0 0
B)What is the probability of selecting a person at random that has a dog but not a cat?(4 points)
Responses

166296=0.561
166 over 296 is equal to 0 point 5 6 1

96500=0.192
96 over 500 is equal to 0 point 1 9 2

134500=0.268
134 over 500 is equal to 0 point 2 6 8

166500=0.332
166 over 500 is equal to 0 point 3 3 2
C)What is the probability of selecting a person at random that has a dog given that they have a cat?(4 points)
Responses

200500=0.400
200 over 500 is equal to 0 point 4 0 0

200334=0.599
200 over 334 is equal to 0 point 5 9 9

200296=0.676
200 over 296 is equal to 0 point 6 7 6

96166=0.578
96 over 166 is equal to 0 point 5 7 8

pick the correct answer for each question.

Answer 1

Question 1:
- x4−−√3=x34
- x3−−√=x23

Question 2:
- 64x5−−−−√
- 64x3

Question 3:
- Exponential Growth:
- f(x)=3x
- f(x)=12(2.1)x
- f(x)=7(15)x

- Exponential Decay:
- f(x)=3(0.66)x

Question 4:
- x-intercept: (-6,0)
- y-intercept: (0, -1)

Question 5:
- (-3, -5)

Question 6:
- Not provided

Question 7:
- g(x) has the greater maximum value because its maximum is 3 and the maximum of f(x) is -3

Question 8:
- 2

Question 9:
- Probability of selecting a person at random that has a dog: 204/500 = 0.408
- Probability of selecting a person at random that has a dog but not a cat: 134/500 = 0.268
- Probability of selecting a person at random that has a dog given that they have a cat: 200/334 = 0.599