Question

Question #ce587

Answer 1

`f(x) = x^2` is an even function.

Explanation:

Graphical proof:

An even function is symmetric about the y-axis. The graph of `f(x) = x^2` shows that the parabola is symmetric about the y-axis: graph{x^2 [-6, 6, -1, 7]}
Therefore, the function is even.

Algebraic proof:

An function `f` is even if the following is true:

`f(-x) = f(x)`

In words, this means, "If you plug is negative `x` (`-x`) for `x` in the function, you will get the original function back."

Let's see if that's true:

`f(x) = x^2`
`f(-x) = (-x)^2`
`= (-1 * x)^2`
`= (-1)^2*x^2`
`= 1*x^2`
`= x^2`

We got the original function `f(x) = x^2` back, so that means that the function is even.