Functions and their curves 183
For example, if f(x)=(x− 1 )^2 ,anda=
1
2
,then
f(ax)=
(x
2
− 1
) 2
.
Both of these curves are shown in Fig. 18.17(a).
Similarly, y=cosx and y=cos2x are shown in
Fig. 18.17(b).
(v)y=−f(x)
The graph of y=−f(x) is obtained by reflecting
y=f(x)in thex-axis. For example, graphs ofy=ex
andy=−exare shown in Fig. 18.18(a) and graphs of
y=x^2 +2andy=−(x^2 + 2 )areshowninFig.18.18(b).
1.0
2 1.0
0
4
(a)
(b)
2
22 042 6
y 5 ( 2 x^21 )^2
x
y 5 cosx y 5 cos 2x
2 2
3 2
x
y 5 (x 2 1)^2
y
y
Figure 18.17
(a)
y
21 x
y 5 ex
y 52 ex
1
Figure 18.18
(b)
y
(^22) x
24
28
211
4
8
0 2
y 52 (x^21 2)
y 5 x^212
Figure 18.18(Continued)
(vi)y=f(−x)
The graph of y=f(−x)is obtained by reflecting
y=f(x)in they-axis. For example, graphs ofy=x^3
and y=(−x)^3 =−x^3 are shown in Fig. 18.19(a)
(a)
10
0
20
220
210
23 2223
(b)
2110
y 5 ( 2 x)^3
y 5 x^3
y 52 Inx
y 5 Inx
y
x
y
x
Figure 18.19