Exploring Absolute Value Graphs and Transformations

This video tutorial covers the basics of graphing absolute value functions and their transformations using Desmos. It explains the role of parameters h and k in shifting the graph and how to use sliders to visualize these changes. The tutorial also guides students on constructing equations to match given points and emphasizes the importance of understanding the axis of symmetry. Additionally, it discusses the effects of changing the value of h on the graph's position and provides examples of graphing functions with specific transformations.

What is the equation of the absolute value function?

• y = 1/x

• y = |x|

• y = x

• y = x^2

What does the red line represent in the graph of an absolute value function?

• The axis of symmetry

• The y-axis

• The x-axis

• The vertex

What effect does the parameter 'a' have on the absolute value function?

• Moves the graph left or right

• Moves the graph up or down

• Changes the width and orientation of the graph

• Changes the color of the graph

If the value of 'h' is increased, in which direction does the vertex move?

• Right

• Left

• Down

• Up

Which parameter moves the vertex up or down?

• x

• a

• h

• k

What is the vertex form of an absolute value function?

• y = a(x + h)^2 - k

• y = a|x + h| - k

• y = a(x - h)^2 + k

• y = a|x - h| + k

If h = -4, how should it be written in the absolute value function?

• x + (-4)

• x - (-4)

• x + 4

• x - 4

What does changing the value of 'h' do to the graph?

• Reflects it over the y-axis

• Changes its width

• Moves it left or right

• Moves it up or down

What is the effect of translating the parent function two units to the right and three units down?

• y = |x + 2| + 3

• y = |x + 2| - 3

• y = |x - 2| + 3

• y = |x - 2| - 3

What is the axis of symmetry for the parent function y = |x|?

• y = 1

• x = 0

• y = 0

• x = 1