Question 1

Which of the following statements is TRUE about the domain and range of the exponential function $$f(x) = a^x$$ for $$a \u003e 1$$?

Accepted Answer

The domain is $$(-\infty, \infty)$$ and the range is $$(0, \infty).$$

Question 2

What is the value of $$\log_5$(25)$$?

Accepted Answer

$$2$$

Question 3

Which of the following best describes the relationship between $$f(x) = a^x$$ and $$f^{-1}(x$$) = \log_a(x)$$?

Accepted Answer

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

Question 4

If $$f(x) = \log_2$(x-1) + 2$$, what is the $$x-$$intercept of the function?

Accepted Answer

$$x = 5$$

Question 5

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

Accepted Answer

$$(0, \infty)$$

Question 6

What is the value of $$\log_9$(1/3)$$?

Accepted Answer

$$-2$$

Question 7

Which transformation is applied to the graph of $$y = \log(x) to $$obtain $$y = \log(x-2)$$?

Accepted Answer

Shift right by 2 units

Question 8

If $$f(x) = \log_a(x)$$ and $$a \u003c 1$$, which of the following best describes the graph of $$f(x)$$?

Accepted Answer

It decreases as $$x$$ increases.

Question 9

What is the $$y-$$intercept of the function $$f(x) = \log(x)$$?

Accepted Answer

There is no $$y-$$intercept.

Question 10

Which of the following statements about the natural logarithm is TRUE?

Accepted Answer

The natural logarithm is defined as $$\ln(x) = \log_e(x).$$

Question 11

If $$f(x) = \log(x+1)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(-1, \infty)$$

Question 12

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

Accepted Answer

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

Question 13

What is the value of $$\log_4$(1/2)$$?

Accepted Answer

$$-1$$

Question 14

Which of the following is a property of the function $$f(x) = \log(x)$$?

Accepted Answer

It has a vertical asymptote at $$x = 0.$$

Question 15

If $$f(x) = \log(x)$$ and $$g(x) = \log(x-3)$$, how is the graph of $$g(x)$$ related to $$f(x)$$?

Accepted Answer

It is shifted right by 3 units.

Question 16

Which of the following is the correct definition of a common logarithm?

Accepted Answer

A logarithm with base $$10.$$

Question 17

If $$\log_a(x) = y$$, which of the following is equivalent to $$x$$?

Accepted Answer

$$x = a^y$$

Question 18

Which of the following is NOT a property of $$f(x) = a^x$$ for $$a \u003e 1$$?

Accepted Answer

The range is $$(-\infty, \infty).$$

Question 19

If $$f(x) = \log(x)$$, what is the effect of the transformation $$f(x) + 2$$?

Accepted Answer

The graph shifts up by 2 units.

Question 20

Which of the following is the correct value of $$\log_2$(1/8)$$?

Accepted Answer

$$-3$$

Logarithmic Functions: Definitions, Properties, and Graphs

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