Use Absolute Value Functions and Transformations Objectives: 1.To evaluate, write, and graph piecewise functions 2.To graph an absolute value function by performing SRT transformations on the parent 3.To apply SRT transformations to graphing any function

You will be able to evaluate, write, and graph piecewise functions

Exercise 1 Determine whether the graph shown represents a function.

Piecewise Functions piecewise function A piecewise function is defined by more than one equation. Each equation corresponds to a different part of the domain of the function.

Exercise 2 Evaluate g ( x ) at the values below. 1. g (1) 2. g (5) 3. g ( − 3)

Exercise 3 Graph g ( x ).

Graphing Piecewise Functions

Method 2: 1.Graph one of the equations in the piecewise function as you normally would. 2.Erase the part of the graph that you don’t need according to the domain of the piece. 3.Repeat for each piece of your function.

Exercise 4

Write a piecewise function for the graph shown.

Parent Function: The simplest member of a family of functions

Parent Functions family of functions parent function Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function. Family of Linear FunctionsLinear Parent Function

Parent Functions family of functions parent function Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function. Family of Quadratic FunctionsQuadratic Parent Function

Parent Functions family of functions parent function Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function. Family of Absolute Value Functions Absolute Value Parent Function

Parent Functions family of functions parent function Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function. Family of FunctionsParent Function A group of functions that share common characteristics Simplest member of the family

Building the Absolute Value Function

parent function This is the absolute value parent function.

Parent Function V-Shape The vertex is the minimum point

Objective 2 You will be able to graph absolute value functions using SRT transformations on the parent function.

Objective 2a You will be able to perform vertical and horizontal shifts on the graph of a function

Translation translation A translation is a transformation that shifts a graph horizontally or vertically, but doesn’t change the overall shape or orientation.

Translation

You will be able to vertically scale the graph of a function

Stretching and Shrinking

You will be able to reflect the graph of a function across the x -axis

Reflection

Minuses and Pluses Just think of the Point-Slope Form:

Minuses and Pluses Just think of the Point-Slope Form:

Objective 2 You will be able to graph absolute value functions using SRT transformations on the parent function.

Multiple Transformations Here are two methods that you could use to graph and absolute value function. The first method will only work for absolute value functions. The second is more general and will work for any function.

Step 4Step 3Step 2Step 1 Graphing Absolute Value Functions Use symmetry to find reflected point Connect the dots in a V-shape

Exercise 6

You will be able to use SRT transformations to graph any function

Multiple Transformations: SRT

Exercise 7

Use Absolute Value Functions and Transformations Objectives: 1.To evaluate, write, and graph piecewise functions 2.To graph an absolute value function by performing SRT transformations on the parent 3.To apply SRT transformations to graphing any function