Question

How do you determine whether `f(t)= t^2 + 2t + -3` is an odd or even function?

Answer 1

This function is neither odd or even.

Explanation:

To test whether a function is odd or even, substitute `-t` for `t`.

`f(t) = (-t)^2 + 2(-t) + -3`
`f(t) = t^2 - 2t - 3`

If it's even, you would get the same equation as you started with. If it's odd, you would get the opposite signs in the equation that you started with. This function would be odd if substituting `-t` gave you `-t^2 - 2t + (-3)`

You could also graph the function to check. It is even if the graph is symmetric with respect to the y-axis, and odd if the graph is symmetric with respect to the origin.