What are even and odd functions?

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Answer 1 · 2014-11-12T20:25:13

Even & Odd Functions

A function #f(x)# is said to be #{("even if "f(-x)=f(x)),("odd if "f(-x)=-f(x)):}#

Note that the graph of an even function is symmetric about the #y#-axis, and the graph of an odd function is symmetric about the origin.

Examples

#f(x)=x^4+3x^2+5# is an even function since

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

#g(x)=x^5-x^3+2x# is an odd function since

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

I hope that this was helpful.