How do you determine if $f (x) = {(x - 3)}^{2}$ $f(x)= (x-3)^2$ is an even or odd function?

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Answer 1 · 2016-06-21T19:23:05

An even function has the property that

$f (- x) = f (x)$ $f(-x)=f(x)$

an odd function has the property that

$f (- x) = - f (x)$ $f(-x)=-f(x)$ .

This function is neither even nor odd.

We can try with a value, for example $x = 1$ $x=1$

$f (1) = {(1 - 3)}^{2} = {(- 2)}^{2} = 4$ $f(1)=(1-3)^2=(-2)^2=4$ .

Now we try with $x = - 1$ $x=-1$

$f (- 1) = {(- 1 - 3)}^{2} = {(- 4)}^{2} = 16$ $f(-1)=(-1-3)^2=(-4)^2=16$

then none of the two conditions is verified.

How do you determine if f(x)= (x-3)^2f(x)=(x−3)2f(x)= (x-3)^2 is an even or odd function?