Transformations of Absolute Value Functions

The video tutorial covers graphing absolute value functions, focusing on the V-shaped graph and its transformations. It explains how to apply transformations using the formula y = a * (x - H) + K, detailing the effects of a, H, and K on the graph. The tutorial also discusses how to identify and apply transformations, including shifting, stretching, and compressing the graph. Key concepts such as the vertex and the impact of positive and negative values on graph orientation are highlighted.

What shape does the graph of an absolute value function typically have?

• W-shaped

• U-shaped

• V-shaped

• S-shaped

What is the absolute value of -2?

• 4

• 2

• 0

• -2

Which of the following represents a transformation of the absolute value function?

• y = x^2

• y = |x| + 3

• y = x + 2

• y = 2x

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

• Vertical shift

• Reflection

• Horizontal shift

• Stretch factor

What effect does a negative 'a' have on the graph of an absolute value function?

• Reflects over the y-axis

• Reflects over the x-axis

• Shifts up

• Shifts down

How can you rewrite x + 2 in the form x - h?

• x + 2

• x - (-2)

• x - 2

• x + (-2)

If 'a' is 1/3, how does the graph of the absolute value function change?

• Stretches horizontally

• Stretches vertically

• Compresses vertically

• Compresses horizontally

What is the effect of 'k' in the transformation formula?

• Moves the graph left or right

• Moves the graph up or down

• Reflects the graph

• Changes the slope

What is the vertex of the absolute value function y = |x - 3| + 2?

• (3, 2)

• (-3, 2)

• (3, -2)

• (-3, -2)

How does the graph of y = |x| change when transformed to y = |x - 4|?

• Shifts 4 units down

• Shifts 4 units left

• Shifts 4 units right

• Shifts 4 units up