Transformations of Absolute Value Functions

The video tutorial covers the concept of absolute value graphs, starting with the basic parent graph and its properties. It explains how to translate graphs using transformations, including horizontal and vertical shifts. The tutorial provides examples of graphing absolute value functions and discusses how to stretch, shrink, and reflect these graphs. Finally, it demonstrates how to combine multiple transformations to graph complex functions.

What is the slope of the right side of the basic absolute value graph?

• -1

• 1

• 0

• 2

What does a transformation do to a graph?

• Only changes its shape

• Only changes its orientation

• Only changes its size

• Changes its size, shape, or orientation

If a graph is translated horizontally to the right by 2 units, what is the new equation?

• y = |x + 2|

• y = |x - 2|

• y = |x| + 2

• y = |x| - 2

What is the new vertex of the graph y = |x + 4| - 2?

• (-4, 2)

• (4, 2)

• (-4, -2)

• (4, -2)

What happens to the graph when the value of 'a' is greater than 1?

• It remains unchanged

• It stretches vertically

• It shrinks vertically

• It flips upside down

What is the effect on the graph when 'a' is less than 1 but greater than 0?

• It remains unchanged

• It stretches vertically

• It shrinks vertically

• It flips upside down

How does the graph of y = -3|x| compare to the parent graph?

• It is reflected and stretched

• It is reflected and shrunk

• It is only stretched

• It is only reflected

What is the effect of a negative 'a' value on the graph?

• It stretches the graph

• It shrinks the graph

• It reflects the graph

• It shifts the graph

In the equation y = a|x - h| + k, what does 'h' represent?

• Reflection

• Vertical shift

• Horizontal shift

• Stretch factor

What is the combined effect of a negative 'a' and a positive 'k' in the equation y = a|x - h| + k?

• Reflection and vertical shift up

• Reflection and vertical shift down

• Stretch and vertical shift up

• Stretch and vertical shift down