Understanding Absolute Value Functions

The video tutorial covers absolute value functions on a coordinate plane, starting with an introduction to their characteristics and standard form. It explains how to graph these functions, focusing on vertex shifts and slope analysis. The tutorial includes examples of graphing with different slopes, including complex cases and negative slopes, highlighting how these affect the graph's shape and orientation.

What is the primary focus of learning absolute value on a coordinate plane?

• Studying the properties of quadratic functions

• Understanding the distance on the x-axis

• Graphing absolute value functions using both x and y axes

• Learning about the slope of a line

What shape do all absolute value graphs have?

• L-shaped

• V-shaped

• U-shaped

• S-shaped

In the parent function of an absolute value, what is the slope for x values less than zero?

• Positive 1

• Negative 1

• Zero

• Undefined

What does the parameter 'a' indicate in the standard form of an absolute value function?

• The vertical shift

• The horizontal shift

• The slope value

• The vertex position

How does the parameter 'h' affect the graph of an absolute value function?

• It shifts the graph up or down

• It changes the slope

• It reflects the graph over the x-axis

• It shifts the graph left or right

In the example f(x) = |x - 3|, what is the new vertex of the graph?

• (-3, 0)

• (3, 0)

• (0, 0)

• (0, 3)

What is the slope on the right side of the graph for the function f(x) = |x - 3|?

• Negative 1

• Zero

• Positive 2

• Positive 1

In the example f(x) = |x| - 2, what is the effect of the parameter 'k'?

• Shifts the graph down

• Shifts the graph right

• Shifts the graph up

• Shifts the graph left

What is the vertex of the function f(x) = |x| - 2?

• (0, 0)

• (0, -2)

• (2, 0)

• (-2, 0)

In the function f(x) = 2|x + 2| - 3, what is the vertex of the graph?

• (-3, -2)

• (-2, -3)

• (0, 0)

• (2, 3)