Shifting Absolute Value Graphs Explained

The video tutorial explains the graph of y = |x|, demonstrating how to calculate absolute values for different x values. It then explores how the equation changes when the graph is shifted three units to the right and four units up, providing a step-by-step explanation of the transformations and their effects on the graph's equation.

What is the absolute value of -2?

• 2

• 0

• 1

• -2

What happens to the graph of y = |x| when it is shifted three units to the right?

• It moves three units up

• It moves three units down

• It moves three units to the left

• It moves three units to the right

At which x-value does the graph of y = |x - 3| switch signs?

• x = 3

• x = 4

• x = 0

• x = -3

What is the value of y when x = 4 in the equation y = |x - 3|?

• 3

• 2

• 1

• 0

How do you modify the equation y = |x| to shift the graph three units to the right?

• Subtract 3 from the equation

• Replace x with x + 3

• Replace x with x - 3

• Add 3 to the equation

What is the new y-value when the graph is shifted four units up?

• 4

• 7

• 3

• 0

How do you modify the equation y = |x - 3| to shift the graph four units up?

• Subtract 4 from the equation

• Replace x with x - 4

• Replace x with x + 4

• Add 4 to the equation

What is the final equation after shifting the graph three units to the right and four units up?

• y = |x - 3| + 4

• y = |x - 3| - 4

• y = |x + 3| + 4

• y = |x + 3| - 4

What happens to the graph of y = |x| when it is shifted four units up?

• It moves four units to the left

• It moves four units to the right

• It moves four units up

• It moves four units down

If the graph of y = |x| is shifted three units to the right and four units up, what is the y-value when x = 3?

• 0

• 3

• 7

• 4