Question 1

Given the function $$f(x) = \log_2$(x-4)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(4, \infty)$$

Question 2

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

Accepted Answer

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

Question 3

What is the vertical asymptote of the function $$f(x) = \log_3$(x+2)$$?

Accepted Answer

$$x = -2$$

Question 4

If $$f(x) = \log_2$(x-3)$$, what is the $$x-$$intercept of the graph?

Accepted Answer

$$(4, 0)$$

Question 5

Which transformation describes the graph of $$f(x) = -2\log_3$(x+1) + 4$$ compared to $$g(x) = \log_3$(x)$$?

Accepted Answer

Reflected over $$x-$$axis, stretched vertically by 2, shifted left 1, up 4

Question 6

Given $$f(x) = \log_2$(x-5)$$, what is the equation of its inverse?

Accepted Answer

$$f^{-1}(x) = 2^x + 5$

Question 7

For the function $$f(x) = \log_2$(x-7)$$, what is the range?

Accepted Answer

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

Question 8

Which of the following statements is TRUE about the graphs of $$y = b^x$$ and $$y = \log_b(x)$$ for $$b \u003e 1$$?

Accepted Answer

They are reflections of each other over the line $$y = x$$

Question 9

If $$f(x) = \log_2$(x-3)$$, what is the $$y-$$intercept of the graph?

Accepted Answer

There is no $$y-$$intercept

Question 10

Which of the following is equivalent to $$\frac{\log_3$(5)}{\log_3$(2)}$$?

Accepted Answer

$$\log_2$(5)$$

Question 11

Suppose $$f(x) = \log_2$(x-1)$$ and $$g(x) = 2^x + 1. $$Which statement is correct?

Accepted Answer

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

Question 12

What is the effect of the transformation $$f(x) = \log_2$(x+3)$$ compared to $$g(x) = \log_2$(x)$$?

Accepted Answer

Shift left 3 units

Question 13

For $$f(x) = \log_2$(x-4)$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 4$$

Question 14

Which of the following best describes the range of $$f(x) = 2^x$$?

Accepted Answer

$$(0, \infty)$$

Question 15

If $$f(x) = \log_2$(x-3)$$, what is the solution to $$f(x) = 2$$?

Accepted Answer

$$x = 7$$

Question 16

Which of the following is NOT a property of logarithmic functions?

Accepted Answer

Their domain is all real numbers

Question 17

Given $$f(x) = \log_2$(x-3)$$, what is the range of its inverse?

Accepted Answer

$$(0, \infty)$$

Question 18

Which of the following best describes the graph of $$f(x) = \log_2$(-x)$$?

Accepted Answer

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

Question 19

If $$f(x) = \log_2$(x-3)$$, what is the $$x-$$value where $$f(x) is $$undefined?

Accepted Answer

$$x = 3$$

Question 20

Which of the following is the correct sequence for graphing a transformed logarithmic function?

Accepted Answer

Apply horizontal shift, then stretch/compress, then reflect, then vertical shift

C5

Study Guide - Practice Questions