8. Analyzing Graphs of Polynomial Functions
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A function f is an even function when f(- x)=f(x) for all x in its domain. A function f is an odd function when f(- x)=- f(x) for all x in its domain.
Odd
Before we begin, let's recall two important definitions.
(- a)^5 = - a^5
(- a)^3 = - a^3
a(- b)=- a * b
a-(- b)=a+b
f(x) | f(- x) | - f(x) |
---|---|---|
x^5+3x^3-x | - x^5-3x^3+x | - x^5-3x^3+x |
We can see above that - f(x)=f(- x). Therefore, f is an odd function.