Use Absolute Value Functions and Transformations Objectives 1
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
Objective 1 You will be able to evaluate, write, and graph piecewise functions
Exercise 1 Determine whether the graph shown represents a function.
Piecewise Functions 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. 2. 3. g(1) g(5) g(− 3)
Exercise 3 Graph g(x).
Graphing Piecewise Functions •
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 •
Exercise 4 Write a piecewise function for the graph shown.
Parent Function: The simplest member of a family of functions
Parent Functions 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 Functions Linear Parent Function
Parent Functions 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 Functions Quadratic Parent Function
Parent Functions 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 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 Functions Parent Function A group of functions that share common characteristics Simplest member of the family
Building the Absolute Value Function •
Building the Absolute Value Function •
Building the Absolute Value 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.
You will be able to perform vertical and horizontal shifts on the graph of a function Objective 2 a
Translation A translation is a transformation that shifts a graph horizontally or vertically, but doesn’t change the overall shape or orientation.
Translation •
Objective 2 b You will be able to vertically scale the graph of a function
Stretching and Shrinking •
Objective 2 c 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.
Graphing Absolute Value Functions • Step 1 Step 2 Use symmetry to. Step find 3 reflected point Connect the dots 4 in Step a V-shape
Exercise 6 •
Exercise 6
Objective 3 You will be able to use SRT transformations to graph any function
Multiple Transformations: SRT • SRT
Exercise 7 •
Exercise 7 •
Exercise 7 •
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
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