Higher Engineering Mathematics

196 GRAPHS

Figure 19.17

(v)y=−f(x)

The graph of y=−f(x) is obtained by reflect-
ingy=f(x)inthex-axis. For example, graphs of
y=exandy=−exare shown in Fig. 19.18(a) and
graphs ofy=x^2 +2 andy=−(x^2 +2) are shown in
Fig. 19.18(b).

(vi)y=f(−x)

The graph ofy=f(−x) is obtained by reflecting
y=f(x)inthey-axis. For example, graphs ofy=x^3

Figure 19.18

Figure 19.18 (Continued)

andy=(−x)^3 =−x^3 are shown in Fig. 19.19(a)

and graphs ofy=lnxandy=−lnxare shown in

Fig. 19.19(b).

Figure 19.19