Quiz about Absolute Value Function Transformations

Question 1

In the absolute value function $$y=a\left|x-h\right|+k$$ , what does the k-value do? Select ALL that apply.

Accepted Answer

It controls the vertical translation by shifting the graph up or down.

Accepted Answer

It is the y-coordinate of the vertex.

Answer

It controls the horizontal translation by shifting the graph left or right.

Answer

It is the x-coordinate of the vertex.

Answer

The opposite of k is the x-coordinate of the vertex.

Question 2

In the absolute value function $$y=a\left|x-h\right|+k$$ , what does the h-value do? Select ALL that apply.

Accepted Answer

It controls the horizontal translation by shifting the graph left or right.

Accepted Answer

The opposite of h is the x-coordinate of the vertex.

Answer

It controls the vertical translation by shifting the graph up or down.

Answer

It is the x-coordinate of the vertex.

Answer

It is the y-coordinate of the vertex.

Question 3

In the absolute value function $$y=a\left|x-h\right|+k$$ , how does a negative a-value affect the graph?

Accepted Answer

-a will cause the graph to reflect over the x-axis.

Answer

-a will cause the graph to move down.

Answer

-a will cause the graph to move left.

Answer

-a will cause the graph to reflect over the y-axis.

Question 4

In the absolute value function $$y=a\left|x-h\right|+k$$ , how does the a-value affect the dilation of the graph? Select ALL that apply.

Accepted Answer

If a is smaller than -1, the graph gets narrower.

Accepted Answer

If a is bigger than 1, the graph gets narrower.

Accepted Answer

If a falls between -1 and 1, the graph will get wider.

Accepted Answer

If $$a=1\ or\ a=-1$$ , the graph will have no dilation.

Answer

If a is bigger than 1, the graph gets wider.

Question 5

Describe the transformations for the function $$y=-\frac{2}{3}\left|x-1\right|$$

Accepted Answer

Translation: right 1

Reflection: over the x-axis

Dilation: wider

Answer

Translation: left 1, down 1

Reflection: over the x-axis

Dilation: wider

Answer

Translation: left 1

Reflection: over the x-axis

Dilation: narrower

Answer

Translation: right 1

Reflection: none

Dilation: narrower

Question 6

Describe the transformations: $$f\left(x\right)=5\left|x+6\right|-1$$

Accepted Answer

Translation: left 6, down 1

Reflection: none

Dilation: narrower

Answer

Translation: up 5

Reflection: none

Dilation: wider

Answer

Translation: right 6, down 1

Reflection: over the x-axis

Dilation: narrower

Answer

Translation: left 6, up 1

Reflection: over the x-axis

Dilation: wider

Question 7

Describe the transformations: $$f\left(x\right)=-\left|x-2\right|+4$$

Accepted Answer

Translation: right 2, up 4

Reflection: over the x-axis

Dilation: none

Answer

Translation: left 2, up 4

Reflection: none

Dilation: wider

Answer

Translation: left 2, down 4

Reflection: over the x-axis

Dilation: none

Answer

Translation: right 2, up 4

Reflection: over the x-axis

Dilation: narrower

Absolute Value Function Transformations

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