1. 2.7 Piecewise Functions

2. What is a Piecewise Function?
• A function that combines pieces of
different equations.
• Each piece is for a different domain
(set of x values).
• Example:

3. Why Are They Important?
• In real life, lots of problems are
modeled by piecewise functions.
• Examples:
▫ Finding shipping costs
▫ Income taxes
▫ Ordering t-shirts

4. Examples:

5. Writing Piecewise Functions
• We know how to graph, now go backwards!
• First, find the domains (where the graph is cut)
• Then, find the slopes and y-intercepts.
• Fill in the equation for each domain.
• Example:
___ x + ___ , if x ______
___ x + ___ , if x ______

6. Example:
___ x + ___ , if x ______
___ x + ___ , if x ______

7. Your Turn!
___ x + ___ , if x ______
___ x + ___ , if x ______

8. Evaluating from a Graph
• Move left/right to the x you need, then move
up/down to find y.
• Example:
• Evaluate f(x) for the function shown when:
• x = -3
• x = -1
•x=2

9. Your Turn!
• Evaluate f(x) for the function shown
when:
•x = -1
•x = 1
•x = 2
•x = 4

10. Evaluating Piecewise Functions
• The domain tells you which equation to use.
• Evaluate f(x) when:
a)x = 0
b)x = 2
c)x = 4

11. Your Turn!
• Evaluate f(x) when:
•x = 0
•x = 3
•x = 6

12. Step Functions
Each piece of the function is a flat,
horizontal line.