Question 1

Which of the following is the correct domain for the function $$f(x) = \log_b x$$ where $$b \u003e 1$$?

Accepted Answer

$$(0, \infty)$$

Question 2

Given the exponential function $$f(x) = 2^x$$, what is the equation of its inverse?

Accepted Answer

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

Question 3

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

Accepted Answer

$$x = 2$$

Question 4

Which transformation will shift the graph of $$f(x) = \log_2$ x$$ three units to the right?

Accepted Answer

$$f(x) = \log_2$(x-3)$$

Question 5

If $$g(x) = -\log_5$(x)$$, which statement best describes its graph compared to $$f(x) = \log_5$(x)$$?

Accepted Answer

It is reflected over the $$x-$$axis.

Question 6

What is the range of the function $$f(x) = \log_4$ x$$?

Accepted Answer

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

Question 7

Which of the following points lies on the graph of $$f(x) = \log_2$ x$$?

Accepted Answer

$$(2, 1)$$

Question 8

Suppose $$h(x) = \log_3$(x+4) - 2. $$What is the domain of $$h(x)$$?

Accepted Answer

$$x \u003e -4$$

Question 9

Which of the following best describes the end behavior of $$f(x) = \log_2$ x as$$ $$x 	o 0^+$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 10

If $$f(x) = \log_2$(x-1)$$, what is the $$x-$$intercept of the graph?

Accepted Answer

$$(2, 0)$$

Question 11

Which of the following describes the effect of $$f(x) = \log_2$(x)$$ being transformed to $$g(x) = \log_2$(x) + 4$$?

Accepted Answer

The graph shifts 4 units up.

Question 12

Given $$f(x) = 3^x$$ and $$g(x) = \log_3$ x$$, which statement is true?

Accepted Answer

The range of $$g(x) is$$ $$(-\infty, \infty).$$

Question 13

Which of the following is the correct equation for reflecting $$f(x) = \log_2$ x$$ over the $$y-$$axis?

Accepted Answer

$$f(x) = \log_2$(-x)$$

Question 14

If $$f(x) = \log_2$(x-5)$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 5$$

Question 15

Which of the following best describes the range of $$f(x) = \log_7$(x-3)$$?

Accepted Answer

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

Question 16

If $$f(x) = \log_2$(x)$$ and $$g(x) = \log_2$(x-4)$$, how is the graph of $$g(x)$$ related to $$f(x)$$?

Accepted Answer

Shifted 4 units to the right

Question 17

Which of the following is the correct range for the exponential function $$f(x) = 2^x$$?

Accepted Answer

$$(0, \infty)$$

Question 18

If $$f(x) = \log_3$(x+2)$$, what is the $$x-$$intercept of the graph?

Accepted Answer

$$(-2, 0)$$

Question 19

Which of the following statements is true about the graph of $$f(x) = \log_2$ x$$?

Accepted Answer

It passes through $$(1, 0).$$

Question 20

If $$f(x) = \log_2$(x)$$, which of the following describes the behavior as $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Graphing Logarithmic Functions: Properties, Transformations, and Examples

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