1. CHAPTER 1.7
Piecewise Functions

2. Piecewise Functions
Different equations used for different intervals of the domain

3. 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

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

5. 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)

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

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

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

9. Graph the tax brackets for different incomes

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

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