Transformations of the Absolute Value Function

The video tutorial explains how to transform the graph of y=|x| by reflecting it across the x-axis and scaling it vertically by a factor of seven. The instructor first visualizes the original graph, then describes the reflection process, resulting in y=-|x|. Next, the graph is scaled vertically, leading to the final equation y=-7|x|. The tutorial concludes with a visual representation of the transformed graph, emphasizing the effects of each transformation step.

How does the graph of y = |x| behave for negative values of x?

• It becomes negative

• It becomes zero

• It remains the same as positive x values

• It mirrors the positive x values

What is the slope of the graph of y = |x| for non-negative x values?

• 0

• -1

• Undefined

• 1

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

• Scaling horizontally

• Reflection across the y-axis

• Translation along the x-axis

• Reflection across the x-axis

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

• The graph shifts downwards

• The graph shifts upwards

• The graph becomes y = -|x|

• The graph becomes y = |x|

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

• It rotates 90 degrees

• It flips vertically

• It remains unchanged

• It flips horizontally

What is the equation of the graph after it is reflected across the x-axis?

• y = |x|

• y = -7|x|

• y = -|x|

• y = 7|x|

What is the final equation after reflecting y = |x| across the x-axis and scaling it vertically by 7?

• y = -|x|

• y = 7|x|

• y = |x|

• y = -7|x|

What happens to the graph when it is scaled vertically by a factor of seven?

• It becomes wider

• It becomes narrower

• It stretches vertically

• It compresses vertically

What is the result of multiplying the y-values by seven in the transformation process?

• The graph shifts to the left

• The graph shifts to the right

• The graph compresses horizontally

• The graph stretches vertically

How does the graph change if scaled by a factor less than one?

• It remains the same

• It becomes narrower

• It becomes wider

• It becomes taller