Name ______________________________________________
Date _______________
Summary of Functions
Understanding Piecewise-Defined Functions
Independent Practice
1.
Consider the following piecewise function and the graph that represents the
function.
f
(
x
)
=
{
x
2
−
1,
whenx≤
0
3
x
+
2,
whenx
>
0
Part A:
Label the pieces of the
f
(
x
)
on the graph.
Part B:
What does the closed circle represent?
Part C:
What does the open circle represent?
Part D:
Give the domain for which the graph is linear.
Part E
:
Give the domain for which the graph is nonlinear (curved).
AlgebraNation.com

2.
Students at a local high school in New York City were reviewing piecewise
functions as part of the NY State Common Core Mathematics Curriculum
tutoring program. They came across this graph.
Part A:
How many pieces are in the step function?
Part B:
How many intervals make up the step function? What are the interval
values?
Part C
: Why do we use open circles in some situations and closed circles in