Higher Engineering Mathematics, Sixth Edition

Functions and their curves 185

 4

10

20

y(x2)^3

(c)

–10

–20

 (^202) x
y
 4
10
20
y 5 (x2)^3
(d)
–10
–20
 (^202) x
y
Figure 18.22(Continued)
Figure 18.22(c) shows a graph ofy=−(x+ 2 )^3
(see−f(x), Section (v) above). Figure 18.22(d)
shows the graph of y= 5 −(x+ 2 )^3 (see
f(x)+a, Section (ii) above).
(b) Figure 18.23(a) shows a graph of y=sinx.
Figure 18.23(b) shows a graph of y=sin2x
(seef(ax), Section (iv) above).
Figure 18.23(c) shows a graph ofy=3sin2x(see
af(x),Section(i)above).Figure18.23(d)showsa
graph ofy= 1 +3sin2x(seef(x)+a,Section (ii)
above).
y 5 sin x
y
x
1
21

2
3 
2

(a)
0
y 5 sin 2x
y
x
1
21

2 32 
 2 
(b)
0
y 5 3 sin 2x
y
x
1
2
3
21
22
23

2
3 
2
^2 
(c)
0
y 1 3 sin 2x
y
x
1
2
3
4
 1
 2

2
3 
2
 2 
(d)
0
Figure 18.23