Exploring Absolute Value Graphs

The video tutorial provides a comprehensive review of absolute value graphs, focusing on transformations such as horizontal and vertical shifts, reflections, and stretches. It explains how these transformations affect the graph's vertex and slopes, and offers graphing techniques and shortcuts for efficient visualization. The tutorial includes examples to illustrate these concepts, helping students understand how to apply transformations to absolute value graphs.

What is the basic equation for an absolute value graph?

• y = x^2

• y = |x|

• y = x

• y = 2x

What does a horizontal shift to the right by 3 units look like in the equation?

• y = |x| - 3

• y = 3|x|

• y = |x - 3|

• y = |x + 3|

How does a vertical stretch by 2 affect the graph of y = |x|?

• It makes the graph wider.

• It shifts the graph to the right.

• It makes the graph steeper.

• It shifts the graph down.

What transformation does a negative sign in front of the absolute value function cause?

• Vertical shift

• Reflection over the x-axis

• Horizontal shift

• Vertical stretch

If the vertex of the basic absolute value graph is at (0,0), where will the vertex be after a horizontal shift left by 5 and a vertical shift up by 3?

• (5, 3)

• (0, 3)

• (-5, 3)

• (-5, -3)

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

• (-4, 0)

• (0, 4)

• (4, 0)

• (0, 0)

What does a vertical shrink by 1/2 do to the graph of y = |x|?

• Shifts the graph down

• Shifts the graph up

• Makes the graph wider

• Makes the graph steeper

If the vertex of the basic absolute value graph is at (0,0), where will the vertex be after a vertical shift up by 4?

• (-4, 0)

• (0, -4)

• (4, 0)

• (0, 4)

What is the slope of the graph y = -1/2|x|?

• 1/2 and -1/2

• 2 and -2

• 1 and -1

• -1/2 and 1/2

What is the effect of a negative sign in front of the absolute value function on the direction the graph opens?

• Opens up

• Opens down

• Shifts left

• Shifts right