Question 1

Which of the following describes the vertical asymptote and the domain of the function

f(x) = \log_{3}(x - 4) + 2

?

Accepted Answer

Vertical Asymptote:

f(x) = \log_{3}(x - 4) + 2

, Domain:

(4, \infty)

Answer

Vertical Asymptote:

f(x) = \log_{3}(x - 4) + 2

, Domain:

(4, \infty)

Answer

Vertical Asymptote:

f(x) = \log_{3}(x - 4) + 2

, Domain:

(4, \infty)

Answer

Vertical Asymptote:

f(x) = \log_{3}(x - 4) + 2

, Domain:

(4, \infty)

Question 2

If the parent function

f(x) = \log_{3}(x - 4) + 2

is transformed into

(4, \infty)

, which statement correctly describes the transformations applied to the graph?

Accepted Answer

A reflection over the x-axis and a horizontal shift 3 units to the left.

Answer

A reflection over the y-axis and a horizontal shift 3 units to the left.

Answer

A reflection over the y-axis and a horizontal shift 3 units to the right.

Answer

A reflection over the x-axis and a vertical shift 3 units up.

Question 3

Which of the following points must lie on the graph of the function

f(x) = \log_{3}(x - 4) + 2

?

Accepted Answer

Answer

Answer

Answer

Question 4

What is the x-intercept of the function

f(x) = \log_{3}(x - 4) + 2

?

Accepted Answer

Answer

Answer

Answer

Question 5

Which of the following describes the end behavior of the function

f(x) = \log_{3}(x - 4) + 2

as

(4, \infty)

approaches

0

from the right?

Accepted Answer

As

f(x) = \log_{3}(x - 4) + 2

,

(4, \infty)

Answer

As

f(x) = \log_{3}(x - 4) + 2

,

(4, \infty)

Answer

As

f(x) = \log_{3}(x - 4) + 2

,

(4, \infty)

Answer

As

f(x) = \log_{3}(x - 4) + 2

,

(4, \infty)

Question 6

Which of the following graphs could represent the function

f(x) = \log_{3}(x - 4) + 2

?

Accepted Answer

A curve that is always decreasing, passing through

f(x) = \log_{3}(x - 4) + 2

with a vertical asymptote at

(4, \infty)

.

Answer

A curve that is always decreasing, passing through

f(x) = \log_{3}(x - 4) + 2

with a horizontal asymptote at

(4, \infty)

.

Answer

A curve that is always increasing, passing through

f(x) = \log_{3}(x - 4) + 2

with a vertical asymptote at

(4, \infty)

.

Answer

A curve that is always increasing, passing through

f(x) = \log_{3}(x - 4) + 2

with a vertical asymptote at

(4, \infty)

.

Question 7

What is the range of the function

f(x) = \log_{3}(x - 4) + 2

?

Accepted Answer

<math>(-\infty, \infty)</math>

Answer

<math>(-\infty, -7)</math>

Answer

<math>(-7, \infty)</math>

Answer

<math>(-5, \infty)</math>

Question 8

Given the function

f(x) = \log_{3}(x - 4) + 2

, at what point does the graph cross the y-axis?

Accepted Answer

Answer

Answer

Answer

Question 9

Which of the following functions matches a graph that has a vertical asymptote at

f(x) = \log_{3}(x - 4) + 2

and passes through the point

(4, \infty)

?

Accepted Answer

Answer

Answer

Answer

Question 10

Which of the following describes the graph of

f(x) = \log_{3}(x - 4) + 2

compared to its parent function

(4, \infty)

?

Accepted Answer

A reflection across the y-axis.

Answer

A reflection across the line

f(x) = \log_{3}(x - 4) + 2

.

Answer

A reflection across the x-axis.

Answer

A horizontal shift 1 unit to the left.

Related quizzes

Related quizzes