1. AMDM 5
Piecewise Functions
Unit

2. Piecewise functions
Piecewise functions are functions defined in pieces over different intervals of the x-axis (domain).

3. Piecewise Functions
Example: The fees to park in the East Economy Garage at Sky Harbor International Airport in Phoenix for a single day:
0 minutes through 60 minutes, the fee is $4.00
60 through 120 minutes, the fee is $8.00
Over 120 minutes (for one day), the fee is $10.00
Table 7.6

4. Piecewise Functions
Graphing this information we see that F(m) (function in minutes) is a discontinuous combination of three linear functions.
Sky Harbor International Airport Parking Fees
Figure 7.13

5. Continuous vs Discontinuous
Continuous function – when the graph of a function is a continuous unbroken line. The graph can be drawn without picking up your pencil.
Discontinuous function – graphs of functions that are not connected.
1/23/2020
AMDM - Piecewise Functions

6. Piecewise Functions
An open circle indicates a value is not included in the function, and a closed circle means the value is included. An arrow indicates the function continues beyond the graph.
Sky Harbor International Airport Parking Fees
Figure 7.13

7. Piecewise Functions
A combination of functions such as the parking fee function is called a piecewise function.

8. Defining a Piecewise Function with an Equation
To model the parking-fee schedule using an algebraic equation, look again at the different pieces that define F(m). For example, for any time up to and including 60 minutes, the parking fee is $4.00. We write
Combining the separate equations for each level of parking fees, we have
It is important to note that F(m) is a single function defined in many pieces, not many functions.

9. Example – Creating and Using a Piecewise Function
The cost of renting a canoe is $20 for the first 4 hours and $5 per hour for each additional hour. Sketch a graph of renting a canoe from 0 to 8 hours, then write a piecewise function for the graph.
Cost
Time in hours

10. Example – Creating and Using a Piecewise Function
David is completing a 100 mile triathalon. He swims 2 miles in 1 hour, bikes 80 miles in 4 hours, and runs 18 miles in 3 hours. Sketch a graph of David’s distance versus his time, then write a piecewise function for the graph.
Activity
Time (h)
Dist (m)
Rate (m/h)
Swimming 1 2
Biking 4 80 20
Running 3 18 6
Distance (meters)
Time (hours)