# Math Help - f(t) = t^2 defined for 0 < t <= 2 pi. Even or not?

1. ## f(t) = t^2 defined for 0 < t <= 2 pi. Even or not?

If I substitute -t for t I get back t^2, so this function would appear to be even. However if I sketch the function (attached) it is not symetrical in the y-axis.
So is the sketch correct and if so, is this function even or not?

Thanks for the help

2. $f:A\subset \mathbb{R}\rightarrow \mathbb{R}$ is an even function iff:

(i) $t\in A \Leftrightarrow -t\in A$

(ii) $f(-t)=f(t)\;\;\forall t\in A$

Your function does not satisfy (i).

Fernando Revilla

3. Thanks for the quick response!