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