
Functions and Graphs 2-31
This final graph represents the piecewise function
f x
x
x
x
x
x
( ) ;
;
=
+ − ≤ ≤−
− ≤ ≤
< <
3
5
3 1
1 1
1 9
Example 2.22 Find the domain and range of the piecewise function given below and graph it. f is a
function defined by
f x x x
x x
( ) = + <
= + ≥
2
1 2
3 2
if
if
Solution: Since f is defined for all real values of x, the domain is the set of all real numbers. In
the interval (-¥, 2), the graph of f is a parabola shifted up 1 unit. In addition, this interval is
open at x = 2 and therefore the graph shows an “open point” on the graph at x = 2. In the interval
[2, +¥), the graph is a line with an x-intercept at (3,