5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:46

Review of Precalculus 73

[−10, 10] by [−10, 20]

Figure 5.4-7

Odd and Even Functions

A functionfis an even function if f(−x)= f(x) for allxin the domain. The graph of an
even function is symmetrical with respect to they-axis. If a point (a,b) is on the graph, so
is the point (−a,b). If a function is a polynomial with only even powers, then it is an even
function. (See Figure 5.4-8.)

x

y

f(x)

(−a, b) (a, b)

0

Figure 5.4-8

A functionfis an odd function iff(−x)=−f(x) for allxin the domain. The graph of
an odd function is symmetrical with respect to the origin. If a point (a,b) is on the graph,
so is the point (−a,−b). If a function is a polynomial with only odd powers and a zero
constant, then it is an odd function. (See Figure 5.4-9.)

x

y

f(x)

0

(a, b)

(–a, – b)

Figure 5.4-9

For the following examples, determine if the given functions are even, odd, or neither.