Higher Engineering Mathematics

FUNCTIONS AND THEIR CURVES 197

C

Problem 1. Sketch the following graphs,

showing relevant points:

(a)y=(x−4)^2 (b)y=x^3 − 8

(a) In Fig. 19.20 a graph ofy=x^2 is shown by

the broken line. The graph ofy=(x−4)^2 is

of the formy=f(x+a). Sincea=−4, then

y=(x−4)^2 is translated 4 units to the right of

y=x^2 , parallel to thex-axis.

(See Section (iii) above).

Figure 19.20

(b) In Fig. 19.21 a graph ofy=x^3 is shown by the
broken line. The graph ofy=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).

Figure 19.21

Problem 2. Sketch the following graphs,

showing relevant points:

(a) y= 5 −(x+2)^3 (b) y= 1 +3 sin 2x

(a) Figure 19.22(a) shows a graph of y=x^3.

Figure 19.22(b) shows a graph ofy=(x+2)^3

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

− 2 2

− 10

− 20

10

(^20) y = x^3
x
y
0
(a)
− 2 2
− 10
− 20
10
20
− 4 x
y
(b)
y = (x+2)^3
0
Figure 19.22