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 $b > 1$?

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

Study Guide - Practice Questions