Transformations of Absolute Value Graphs

The video tutorial explains how to transform the graph of y = |x| by reflecting it across the x-axis and then compressing it vertically by a factor of 8/3. It details the steps involved in each transformation, including the mathematical reasoning behind reflection and compression, and how to apply these transformations to obtain the new graph equation.

What is the first transformation applied to the graph of y = |x|?

• Reflection across the y-axis

• Reflection across the x-axis

• Vertical stretch by a factor of 8/3

• Horizontal compression by a factor of 8/3

How does the graph of y = |x| appear in the first quadrant?

• y = x

• y = -2x

• y = -x

• y = 2x

What is the equation of the graph after reflecting y = |x| across the x-axis?

• y = -|x|

• y = -2|x|

• y = 2|x|

• y = |x|

What does compressing a graph vertically by a factor of 8/3 mean?

• Multiplying y-values by 8/3

• Dividing y-values by 8/3

• Dividing x-values by 8/3

• Multiplying x-values by 8/3

What is the reciprocal of 8/3 used for vertical compression?

• 3/8

• 8/3

• 1/8

• 1/3

How do you express vertical compression in terms of multiplication?

• Multiply by 8/3

• Multiply by 1/8

• Multiply by 3/8

• Multiply by 1/3

What is the final equation of the graph after both transformations?

• y = (8/3)|x|

• y = -|x|

• y = (3/8)|x|

• y = -(3/8)|x|

Why do we multiply by the reciprocal when compressing vertically?

• To increase the height of the graph

• To reflect the graph

• To decrease the height of the graph

• To maintain the original height

What happens to the graph when it is compressed vertically?

• It flips upside down

• It remains the same

• It becomes wider

• It becomes narrower

What is the effect of reflecting a graph across the x-axis?

• It moves the graph to the right

• It inverts the graph horizontally

• It moves the graph to the left

• It inverts the graph vertically