Quiz about Chapter 3 Test Review (Big Ideas)

Question 1

Let $$f\left(x\right)=x+3$$ , and let $$g\left(x\right)=f\left(2x\right)$$ . Which description of the transformation from the graph of $$f$$ to the graph of $$g$$ .

Accepted Answer

Horizontal shrink by a factor of $$\frac{1}{2}$$ .

Answer

Horizontal stretch by a factor of 3.

Answer

Horizontal shrink by a factor of $$\frac{1}{3}$$ .

Answer

Horizontal stretch by a factor of 2.

Question 2

Let $$f\left(x\right)=3x-4$$ . Graph $$g\left(x\right)=-f\left(x\right)$$ .

Choose the description of the transformation from the graph of f to the graph of g.

Accepted Answer

The graph of g is a reflection in the x-axis of the graph of f.

Answer

The graph of g is a reflection in the y-axis of the graph of f.

Question 3

Identify the graph of $$g\left(x\right)=\left|x+4\right|$$ .

Accepted Answer

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Question 4

Find the domain and range of $$g\left(x\right)=\left|x-2\right|$$ .

Accepted Answer

domain: all real numbers

range: $$y\ge0$$

Answer

domain: $$x\le0$$

range: all real numbers

Answer

domain: all real numbers

range: $$y\le0$$

Answer

domain: $$x\ge0$$

range: all real numbers

Question 5

Determine when g(x) is positive and negative.

Accepted Answer

Positive: $$x<-3\ and\ x>-3$$

Negative: none

Answer

Positive: none

Negative: $$x<-3\ and\ x>-3$$

Answer

Positive: $$x>3$$

Negative: $$x<3$$

Answer

Positive: $$x>-3$$

Negative: none

Question 6

Determine where g(x) is increasing and decreasing.

Accepted Answer

Increasing: $$x>-3$$

Decreasing: $$x<-3$$

Answer

Increasing: $$x<-3$$

Decreasing: $$x>-3$$

Question 7

Describe the end behavior of g(x).

Accepted Answer

$$y\rightarrow+\infty\ as\ x\rightarrow-\infty\ and\ y\rightarrow+\infty\ as\ x\rightarrow+\infty$$

Answer

$$y\rightarrow-\infty\ as\ x\rightarrow-\infty\ and\ y\rightarrow-\infty\ as\ x\rightarrow+\infty$$

Question 8

Identify the graph of $$g\left(x\right)=\left|x\right|-6$$ .

Accepted Answer

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Question 9

Identify the domain and range.

Accepted Answer

Domain: All real numbers

Range: $$y\ge-2$$

Answer

Domain: $$y\ge-2$$

Range: All real numbers

Answer

Domain: All real numbers

Range: $$y\ge2$$

Answer

Domain: $$y\le2$$

Range: All real numbers

Question 10

Describe the transformation.

Accepted Answer

Horizontal, 4 units left

Answer

Horizontal, 3 units left

Answer

Vertical, 3 units up

Answer

Vertical, 4 units down

Chapter 3 Test Review (Big Ideas)

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