Question 1

Which of the following is the inverse of the function $$f(x) = 2^x$$?

Accepted Answer

$$f^{-1}(x$$) = \$$log_2 x$

Question 2

Given the function $$f(x) = \log_2$(x-3)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(3, \infty)$$

Question 3

What is the $$x-$$intercept of the function $$f(x) = \log_2$(x-4)$$?

Accepted Answer

$$(4, 0)$$

Question 4

Which transformation occurs when the function $$f(x) = \log_2$(x) is $$changed to $$f(x) = \log_2$(x-5)$$?

Accepted Answer

Shift 5 units right

Question 5

For the function $$f(x) = \log_2$(-x)$$, which statement about its graph is correct?

Accepted Answer

It is a reflection of $$\log_2$(x)$$ over the $$y-$$axis

Question 6

What is the vertical asymptote of the function $$f(x) = \log_2$(x+7)$$?

Accepted Answer

$$x = -7$$

Question 7

If $$f(x) = \log_2$(x-2)$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 8

Which of the following is equal to $$\log_2$(8)$$?

Accepted Answer

$$3$$

Question 9

Given $$f(x) = \log_2$(x)$$ and $$g(x) = 2^x$$, which statement is true?

Accepted Answer

$$f$$ and $$g$$ are inverse functions

Question 10

What is the inverse of $$f(x) = \log_2$(x+9)$$?

Accepted Answer

$$f^{-1}(x) = 2^x + 9$

Question 11

Which of the following describes the effect of multiplying the output of $$f(x) = \log_2$(x) by$$ $$3 to $$get $$g(x) = 3\log_2$(x)$$?

Accepted Answer

Vertical stretch by a factor of 3

Question 12

For the function $$f(x) = \log_2$(x-6)$$, what is the $$y-$$intercept?

Accepted Answer

There is no $$y-$$intercept

Question 13

Which of the following is the correct graph for $$f(x) = \log_2$(x)$$?

Accepted Answer

A curve passing through $$(1,0)$$, increasing to the right, with a vertical asymptote at $$x=0$$

Question 14

If $$f(x) = \log_2$(x)$$, what is $$f(16)$$?

Accepted Answer

$$4$$

Question 15

Which of the following is the correct domain for the inverse of $$f(x) = \log_2$(x+9)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 16

A scientist models the population of bacteria with $$P(t) = 2^t. If $$the population reaches $$128$$ after $$t$$ hours, how many hours have passed?

Accepted Answer

$$t = 7$$

Question 17

Which of the following is a property of logarithmic functions $$f(x) = \log_b(x)$$ for $$b \u003e 1$$?

Accepted Answer

The function is increasing and has a vertical asymptote at $$x=0$$

Question 18

Which of the following transformations will shift the graph of $$f(x) = \log_2$(x) up by 4 $$units?

Accepted Answer

$$f(x) = \log_2$(x) + 4$$

Question 19

If $$f(x) = \log_2$(x)$$ and $$g(x) = \log_2$(x-2)$$, how does the graph of $$g(x)$$ compare to $$f(x)$$?

Accepted Answer

It is shifted 2 units right

C5

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