Piecewise-Defined Functions Lesson 2.5

Piecewise Defined Functions Consider a function defined differently for different parts of the domain (the x values) Consider what the table of values looks like

Piecewise Defined Functions x y -1 1 2 3 4

Piecewise Defined Functions Our calculator handles piecewise functions with the when ( ) command What will the graph look like? Use Diamond 0 for the ≤ sign

Piecewise Defined Functions

Piecewise Defined Functions Condition Expression to use when condition is true Expression to use when condition is false

Piecewise Defined Functions Try entering and graphing the following function

Piecewise Defined Functions

Absolute Value Function Whatever you put into the function comes out positive -3 +7 +7 +3

Absolute Value Function Definition Use the abs( ) function on your calculator

Absolute Value Function Note the graph of y = | x | Table of values

Absolute Value Inequalities |a x + b | < k is equivalent to - k < a x + b < k - k < a x + b and a x + b < k 7

Absolute Value Inequalities |a x + b | > k is equivalent to a x + b < -k or a x + b > k 7 ) )

Try It Out! |15 – x | < 7 |5x – 7 | > 2 Solve symbolically Show graphical solution

Assignment Lesson 2.5 Page 133 Exercises 1 – 77 EOO