Question 1

Which of the following describes the sequence of transformations applied to the basic function $$f(x) = |x| to $$obtain $$g(x) = 2|6 - x|$$?

Accepted Answer

Reflect $$f(x)$$ across the $$y-$$axis, shift right by 6 units, and vertically stretch by a factor of 2.

Question 2

What is the domain of the function $$g(x) = 2|6 - x|$$?

Accepted Answer

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

Question 3

What is the range of the function $$g(x) = 2|6 - x|$$?

Accepted Answer

$$[0, \infty)$$

Question 4

Which of the following is a key point on the graph of $$g(x) = 2|6 - x|$$?

Accepted Answer

$$(6, 0)$$

Question 5

If $$g(x) = 2|6 - x|$$, what is the value of $$g(3)$$?

Accepted Answer

$$6$$

Question 6

For the function $$g(x) = 2|6 - x|$$, which statement is true about its symmetry?

Accepted Answer

The function is symmetric about $$x = 6.$$

Question 7

Which of the following best describes the vertex of the graph of $$g(x) = 2|6 - x|$$?

Accepted Answer

The vertex is at $$(6, 0).$$

Question 8

Which of the following points lies on the graph of $$g(x) = 2|6 - x|$$?

Accepted Answer

$$(0, 12)$$

Question 9

If $$g(x) = 2|6 - x|$$, for which value of $$x$$ does $$g(x) = 8$$?

Accepted Answer

$$x = 2 or$$ $$x = 10$$

Question 10

Which of the following real-world scenarios could be modeled by $$g(x) = 2|6 - x|$$?

Accepted Answer

The cost in dollars to travel to a city that is 6 miles away, where each mile away from the city center increases the cost by $2.

Question 11

Which transformation occurs first when graphing $$g(x) = 2|6 - x|$$ from $$f(x) = |x|$$?

Accepted Answer

Reflection across the $$y-$$axis

Question 12

What is the slope of the left side of the graph of $$g(x) = 2|6 - x|$$?

Accepted Answer

$$2$$

Question 13

What is the $$x-$$intercept of the function $$g(x) = 2|6 - x|$$?

Accepted Answer

There is no $$x-$$intercept.

Question 14

If $$g(x) = 2|6 - x|$$, what is the minimum value of $$g(x)$$?

Accepted Answer

$$0$$

Graphing and Analyzing Absolute Value Functions

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