Page 21 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions
Graphs of piecewise functions

A function can be defined differently for different intervals in a given domain. We say that the function is
1 defined piecewise on a domain, or that the function is a piecewise function.
Consider the function f defined by

x + 1 , –1 < x , 0.
f(x) = x 2 , 0 < x , 1,
2 , 1 < x < 2.

We notice that the graph of f has 3 sections or pieces, as shown below. We say that the function f is piecewise
for the domain [–1, 2].

y
2

Sketch Graphs
1
INFO

x
–1 0 1 2
Figure 1.15
Note: • indicates that this point is included;
° indicates that this point is excluded.

Example 12

Sketch the graph of the function f defined by
2
x , –3 < x , 2.
f(x) = 5 , x = 2,
8 – x , 2 , x < 4.

Solution: For –3 < x , 2, the graph is quadratic.
For x = 2, y = 5.
For 2 , x < 4, the graph is straight line.
Hence, the graph of the function f is as shown below.

y
9

6 y = 8 – x
y = x 2
5 y = 5
4

x
–3 0 2 4

18

01a STPM Math T T1.indd 18 3/28/18 4:20 PM