Modeling with Functions - CW 9.3.3 - Mr. Arellano
Name
Per.
*For this assignment, all work must be done on a separate sheet of graph paper*
Piecewise-Defined Functions
Often a situation cannot be described using a single function. When multiple functions are used to describe a
situation, the function is called a piecewise-defined function. Today you will build new functions by using
pieces of familiar functions.
The Horizon Phone Company offers a basic monthly voice plan where customers pay a low monthly fee, but they
must pay extra if their calls exceed the maximum number of minutes. The graph at right shows how the plan
works.
$42.00
1) Describe the plan in detail. How many minutes are included in the
monthly fee? What is the charge for extra minutes?
$41.00
2) Write an equation for the first piece of the graph. What is its domain?
$40.00
3) Use the graph and your description of the plan to write equations for
the second and third pieces of the graph. Write the domain for each
piece.
450
452
454
456
4) Does the graph represent a functional relationship? Explain.
Time (minutes)
5) This kind of piecewise-defined function is called a step function. Why do you think it has that name? What
other situations can be modeled with step functions?
Draw a complete graph of each of the following piecewise-defined functions. It may help to make a table first.
3
-45xx-2
x<1
6)
f(x)=<-1 -2<.52
7)
x>1
5
2
Elisa is training to run a 5-mile fun run. One day she runs from her house to her friend Anna's house two miles
away. Elisa talks to Anna for 10 minutes while she stretches, and then she runs home.
8) Elisa runs at the pace of one mile in 10 minutes on the way to Anna's house. On the way home, she is tired, so
she runs at the pace of one mile in 12 minutes. Draw an accurate graph of her distance from home over time.
9) Should this graph be discrete or continuous? Explain.
10) Now write a piecewise-defined function to represent the graph. Remember to include the domain for each
piece.
