Question 1

Given the function $$f(x) = \log_3$(x - 1)$$, which of the following describes the correct sequence of transformations applied to the parent function $$y = \log_3$ x to $$obtain $$f(x)$$?

Accepted Answer

Shift the graph 1 unit to the right.

Question 2

What is the domain of the function $$f(x) = \log_3$(x - 1)$$?

Accepted Answer

$$x \u003e 1$$

Question 3

What is the range of the function $$f(x) = \log_3$(x - 1)$$?

Accepted Answer

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

Question 4

What is the equation of the vertical asymptote for the function $$f(x) = \log_3$(x - 1)$$?

Accepted Answer

$$x = 1$$

Question 5

If the function $$g(x) = \log_3$(x - 1) + 2$$, which transformation is applied to $$f(x) = \log_3$(x - 1) to $$obtain $$g(x)$$?

Accepted Answer

Shift the graph 2 units up.

Question 6

Suppose $$h(x) = \log_3$(-(x - 1)). $$Which of the following best describes the transformation from $$f(x) = \log_3$(x - 1) to$$ $$h(x)$$?

Accepted Answer

Reflect the graph over the vertical asymptote $$x = 1.$$

Question 7

Which of the following is the $$x-$$intercept of the function $$f(x) = \log_3$(x - 1)$$?

Accepted Answer

$$(2, 0)$$

Question 8

If $$f(x) = \log_3$(x - 1)$$, for which value of $$x$$ does $$f(x) = 2$$?

Accepted Answer

$$x = 10$$

Question 9

Which of the following statements is true about the end behavior of $$f(x) = \log_3$(x - 1) as$$ $$x 	o 1^+$$?

Accepted Answer

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

Question 10

A scientist models the pH of a solution as $$pH = -\log_{10}(H^+)$$, where $$H^+ is $$the hydrogen ion concentration. If $$H^+ = 0.01$$, what is the pH?

Accepted Answer

$$2$$

Question 11

Which of the following best describes the effect of replacing $$x$$ with $$x + 4 in $$the function $$f(x) = \log_3$(x - 1)$$?

Accepted Answer

Shift the graph 4 units to the left.

Question 12

If $$f(x) = \log_3$(x - 1)$$, what is the value of $$f(4)$$?

Accepted Answer

$$\log_3$ 3 = 1$$

Exponential and Logarithmic Functions: Transformations and Properties

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