Graphing Absolute Value Functions

This video tutorial covers graphing absolute value functions, starting with an introduction to absolute value as a measure of distance from zero. It explains how to graph the parent absolute value function and describes its characteristic V shape. The tutorial then explores various transformations, such as reflections and translations, and how they affect the graph. It concludes with more complex transformations and how to write equations for these functions.

What is the absolute value of -5?

• 10

• 5

• 0

• -5

How many units away from zero is the absolute value of 4?

• 2

• 8

• 4

• 6

What shape does the graph of the parent absolute value function form?

• Line

• V-shape

• Circle

• U-shape

What is the domain of the parent absolute value function?

• [0, ∞)

• [0, 1]

• (-∞, 0]

• (-∞, ∞)

What transformation occurs when graphing y = -|x|?

• Reflection across the y-axis

• Reflection across the x-axis

• Translation down

• Translation up

If the vertex of an absolute value function is moved 3 units up, what is the new range?

• [0, ∞)

• (-∞, 0]

• [3, ∞)

• (-∞, 3]

What is the transformation for the function y = |x - 4|?

• 4 units right

• 4 units down

• 4 units left

• 4 units up

What does a vertical stretch by a factor of 2 do to the graph of an absolute value function?

• Makes it wider

• Shifts it up

• Makes it narrower

• Shifts it down

What is the vertex of the function y = |x + 1| - 7?

• (-1, -7)

• (1, -7)

• (-1, 7)

• (1, 7)

What is the equation of an absolute value function with a vertex at (-3, 1) and a slope of -1?

• y = -|x + 3| + 1

• y = |x - 3| - 1

• y = -|x - 3| + 1

• y = |x + 3| - 1