Graphing Absolute Value Functions and Transformations

The video tutorial covers graphing absolute value functions by transforming the parent function. It begins with an introduction to the absolute value parent function and its equation. The tutorial explains how to plot points and identify characteristics like symmetry and vertex. It then explores transformations such as reflections and shifts, and how multipliers affect graph steepness. Finally, it demonstrates how to predict graph shapes from given equations, emphasizing the importance of understanding shifts and steepness changes.

What is the equation of the absolute value parent function?

• y = x

• y = |x|

• y = x^2

• y = 1/x

What is the absolute value of -3?

• 0

• 1

• -3

• 3

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

• V-shape

• W-shape

• U-shape

• S-shape

What is the vertex of the absolute value parent function?

• (1,1)

• (0,0)

• (2,2)

• (-1,-1)

What does the graph of y = -|x| represent?

• A reflection across the y-axis

• A reflection across the x-axis

• A vertical shift

• A horizontal shift

What transformation occurs in the graph of y = |x| - 3?

• 3 units to the right

• 3 units up

• 3 units down

• 3 units to the left

What is the effect of the transformation y = |x - 2|?

• 2 units to the left

• 2 units down

• 2 units up

• 2 units to the right

What happens to the graph of y = 3|x|?

• It shifts 3 units down

• It shifts 3 units up

• It becomes 3 times steeper

• It becomes 3 times wider

What is the vertex of the function y = |x + 2| - 5?

• (-2, -5)

• (2, -5)

• (-2, 5)

• (2, 5)

If a graph is reflected across the x-axis and shifted 2 units up, what is the equation?

• y = |x| + 2

• y = -|x| + 2

• y = |x| - 2

• y = -|x| - 2