196 Higher Engineering Mathematics
22
24 22
24
26
2
2
4
6
(^04) x
y
y 5 x
(^211)
x
y 5 x
(^211)
x
y^5
x
Figure 18.35
18.8 Brief guide to curve sketching
The following steps will give information from which
the graphs of many types of functionsy=f(x)can be
sketched.
(i) Use calculus to determine the location and nature
of maximum and minimum points (see Chap-
ter 28)
(ii) Determine where thecurve cuts thex-andy-axes
(iii) Inspect the equation for symmetry.
(a) If the equation is unchanged when−xis substi-
tuted forx, the graph will be symmetrical about
they-axis (i.e. it is aneven function).
(b) If the equation is unchanged when−yis substi-
tuted fory, the graph will be symmetrical about
thex-axis.
(c) If f(−x)=−f(x), the graph is symmet-
rical about the origin (i.e. it is an odd
function).
(iv) Check for any asymptotes.