Absolute Value Functions
HS Math
Created on September 25, 2024
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Transcript
- Identify reflection, translation, and transformation when graphing absolute value functions.- Write an absolute value function given a graph.-Graph an absolute value function.
Objectives
Absolute Value Functions
The parent absolute value function isf(x) = |x|
An absolute value function changes direction at its vertex.
A function that contains an absolute value!
Absolute Value Function
An absolute value function represents the positive and negative cases for each solution.The vertex is a point of symmetry.f(5) = |5| = 5 give the point (5, 5)f(-5) = |-5| = 5 gives the point (-5, 5)
Absolute Value Function
The axis of symmetry occurs at the vertex.
Absolute Value Function
The axis of symmetry occurs at the vertex.In the parent function, the axis of symmetry is the line x = 0.
Absolute Value Function
A transformation is a change made to the parent function that moves the graph.A translation describes how a function is shifted left or right.
Absolute Value Function
shifts your vertex up or down
shifts your vertex to the left or right.
shrinks or stretches the opening.Think of it as slope!A negative reflects the graph upside down.
Absolute Value Function - Possible Transformations
shrinks or stretches the opening.Think of it as slope!A negative reflects the graph upside down.
Absolute Value Function - Possible Transformations
shrinks or stretches the opening.Think of it as slope!A negative reflects the graph upside down.
Absolute Value Function - Possible Transformations
shrinks or stretches the opening.Think of it as slope!A negative reflects the graph upside down.
Absolute Value Function - Possible Transformations
shifts your vertex up or down
Absolute Value Function - Possible Transformations
Because we have x - h, thehorizontal shift goes the opposite direction of the sign.
BE CAREFUL!
shifts your vertex to the left or right.
Absolute Value Function - Possible Transformations
Put it all together!
Put it all together!
Write the function!
Write the function!
- Identify reflection, translation, and transformation when graphing absolute value functions.- Write an absolute value function given a graph.-Graph an absolute value function.
You should be able to
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