Higher Engineering Mathematics, Sixth Edition

182 Higher Engineering Mathematics

(b)

0

2 2

1

3

 3  2 

ycos 2

ycos



yx

yx 3

6

4

2

0 2 4

(a)

(^6) x
y
(c)
 1120
2
4
6
8
 (^2) x
yx^2  3
yx^2
y
Figure 18.14
0
(a)
(b)
1
1
21
21
0
(x 2 )
y 5 sin x
y 5 sinx
y 5 sin
y 5 sin(x 1 )
2

2

4

4

3

3

4

3



2
3 
2
3 
2 
2 
y
x
x
y
Figure 18.15
Similarly graphs of y=x^2 , y=(x− 1 )^2 and
y=(x+ 2 )^2 are shown in Fig. 18.16.
(iv)y=f(ax)
For each point (x 1 ,y 1 ) on the graph ofy=f(x),there
exists a point
(x 1
a
,y 1
)
on the graph ofy=f(ax). Thus
the graph ofy=f(ax)can be obtained by stretching
y=f(x)parallel to thex-axis by a scale factor
1
a
6
4
2
22 21102
y 5 (x 1 2)^2
y 5 (x 2 1)^2
y 5 x^2
x
y
Figure 18.16