PiecewiseDefined Functions Lesson 2 5 Piecewise Defined Functions

Piecewise-Defined Functions Lesson 2. 5

Piecewise Defined Functions l Consider a function defined differently for different parts of the domain (the x values) l Consider what the table of values looks like 2

Piecewise Defined Functions x y -1 0 1 2 3 4 3

Piecewise Defined Functions l Our calculator handles piecewise functions with the when ( ) command Use Diamond 0 for the ≤ sign What will the graph look like? 4

Piecewise Defined Functions 5

Piecewise Defined Functions l l l Condition Expression to use when condition is true Expression to use when condition is false 6

Piecewise Defined Functions l Try entering and graphing the following function 7

Piecewise Defined Functions 8

Absolute Value Function l Whatever you put into the function comes out positive -3 +7 +3 +7 9

Absolute Value Function l Definition Use the abs( ) function on your calculator 10

Absolute Value Function l Note the graph of y = | x | l Table of values 11

Absolute Value Inequalities l |a x + b | < k is equivalent to l l -k<ax+b<k - k < a x + b and a x + b < k 7 12

Absolute Value Inequalities |a x + b | > k is equivalent to l a x + b < -k or a x + b > k 7 ) ) l 13

Try It Out! l |15 – x | < 7 l l Solve symbolically |5 x – 7 | > 2 l Show graphical solution 14

Assignment l l l Lesson 2. 5 Page 133 Exercises 1 – 77 EOO 15