CHAPTER 1.7 Piecewise Functions

Piecewise Functions Different equations used for different intervals of the domain

Piecewise Functions 1) draw ‘boundary lines’ 2) Graph first line. Erase extra 3. Graph second line. Erase extra F(x)= { 1 if x≤-2 x+2 if -2<x ≤3 2x if x>3

Graph: F(x) = 𝑥+2 𝑖𝑓 𝑥 <1 1 2 𝑥+1 𝑖𝑓 𝑥 ≥1

Evaluate: F(x)= 𝑥 2 𝑖𝑓 𝑥<−2 2𝑥 𝑖𝑓 −2≤𝑥<3 2𝑥+1 𝑖𝑓 𝑥≥3 3) F(-4) 4) F(0) 5) F(3)

Step Function Looks like a set of stairs Breaks in the graph of the function

Greatest Integer Function Type of step function Means the greatest integer not greater than x. Example: [[8.9]]=8 [[-3.9]] = -4

ABSOLUTE VALUE FUNCTION V-shaped PARENT GRAPH (Basic graph)

Graph the tax brackets for different incomes

Tax Bracket (percent) Income ($100,000)

Graph f(x) = 2 x -1 x (x,y)