Higher Engineering Mathematics, Sixth Edition

196 Higher Engineering Mathematics

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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.