Question 1

Which of the following is the domain of the function $$f(x) = \log_3$ x$$?

Accepted Answer

$$x \u003e 0$$

Question 2

What is the range of the function $$f(x) = 3^x$$?

Accepted Answer

$$y \u003e 0$$

Question 3

The graph of $$f(x) = \log_3$ x is $$the reflection of the graph of $$f(x) = 3^x$$ over which line?

Accepted Answer

$$y = x$$

Question 4

Which transformation is applied to $$f(x) = \log_3$ x to $$obtain $$g(x) = \log_3$(x-2)$$?

Accepted Answer

Shift right by 2 units

Question 5

Given $$g(x) = -\log_3$(x+1)$$, which transformation is NOT applied to the parent function $$f(x) = \log_3$ x$$?

Accepted Answer

Vertical stretch

Question 6

What is the equation of the vertical asymptote for the function $$f(x) = \log_3$(x-4)$$?

Accepted Answer

$$x = 4$$

Question 7

If $$f(x) = \log_3$ x$$ and $$g(x) = \log_3$(x+2)$$, how does the graph of $$g(x)$$ compare to $$f(x)$$?

Accepted Answer

Shifted left by 2 units

Question 8

Which of the following statements is true about the range of $$f(x) = \log_3$ x$$?

Accepted Answer

$$y \in \mathbb{R}$$

Question 9

For the function $$f(x) = \log_3$(x-1)$$, what is the domain?

Accepted Answer

$$x \u003e 1$$

Question 10

Which of the following best describes the end behavior of $$f(x) = \log_3$ x as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 11

If $$f(x) = 3^x$$ and $$g(x) = \log_3$ x$$, which of the following is true?

Accepted Answer

$$g(x) is $$the inverse of $$f(x)$$

Question 12

What is the effect of multiplying the parent function $$f(x) = \log_3$ x by$$ $$-1$$?

Accepted Answer

Reflects the graph over the $$x-$$axis

Question 13

Which of the following is the correct range for $$f(x) = \log_3$(x-2)$$?

Accepted Answer

$$y \in \mathbb{R}$$

Question 14

Given $$f(x) = \log_3$(x+4)$$, what is the $$x-$$intercept of the graph?

Accepted Answer

$$x = -3$$

Question 15

Which transformation is applied to $$f(x) = \log_3$ x to $$obtain $$g(x) = \log_3$(x) + 2$$?

Accepted Answer

Shift up by 2 units

Question 16

If $$f(x) = \log_3$(x-1)$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 1$$

Question 17

Which of the following describes the graph of $$f(x) = \log_3$ x$$?

Accepted Answer

Increasing for all $$x \u003e 0$$

Question 18

For the function $$f(x) = \log_3$(x+2)$$, what is the domain?

Accepted Answer

$$x \u003e -2$$

Question 19

Which of the following is true about the graph of $$f(x) = \log_3$ x$$?

Accepted Answer

It passes through the point $$(1, 0)$$

Graphing Logarithmic Functions: Properties, Transformations, and Examples

Study Guide - Practice Questions