Higher Engineering Mathematics, Sixth Edition

184 Higher Engineering Mathematics

and graphs ofy=lnx and y=−lnx are shown in

Fig. 18.19(b).

Problem 1. Sketch the following graphs, showing

relevant points:

(a)y=(x− 4 )^2 (b)y=x^3 − 8

(a) In Fig. 18.20 a graph ofy=x^2 is shown by the bro-

ken line. The graph ofy=(x− 4 )^2 is of the form

y=f(x+a).Sincea=−4, theny=(x− 4 )^2 is

translated 4 units to the right ofy=x^2 , parallel to

thex-axis.

(See Section (iii) above).

yx^2 y(x4)^2

4

 4  2 0

8

2 4 6

y

x

Figure 18.20

(b) In Fig. 18.21 a graph ofy=x^3 isshownbythe

broken line. The graph of y=x^3 −8isofthe

formy=f(x)+a.Sincea=−8, theny=x^3 − 8

is translated 8 units down fromy=x^3 , parallel to

they-axis.

(See Section (ii) above).

20

10

–10

–20

–30

 3  2  11230

yx^3

yx^3  8

y

x

Figure 18.21

Problem 2. Sketch the following graphs, showing

relevant points:

(a)y= 5 −(x+ 2 )^3 (b)y= 1 +3sin2x

(a) Figure 18.22(a) shows a graph of y=x^3.

Figure 18.22(b) shows a graph ofy=(x+ 2 )^3 (see

f(x+a), Section (iii) above).

10

20

yx^3

(a)

–10

–20

 2 02 x

y

24

10

20

y 5 (x 1 2)^3

(b)

–10

–20

(^2202) x
y
Figure 18.22