Question: "What are even and odd functions?"

mierekaslq

Answered question

2022-12-23

What are even and odd functions?

Armeebildzku

Beginner2022-12-24Added 14 answers

Even & Odd Functions
A function

f (x)

is said to be

{\begin{matrix} e v e n if f (- x) = f (x) \\ o d d if f (- x) = - f (x) \end{matrix}

Keep in mind that an even function's graph is symmetrical around the

y

-axis, and the graph of an odd function is symmetric about the origin.
Examples

f (x) = x^{4} + 3 x^{2} + 5

is an even function since

f (- x) = {(- x)}^{4} + {(- x)}^{2} + 5 = x^{4} + 3 x^{2} + 5 = f (x)

g (x) = x^{5} - x^{3} + 2 x

is an odd function since

g (- x) = {(- x)}^{5} - {(- x)}^{3} + 2 (- x) = - x^{5} + x^{3} - 2 x = - f (x)

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