Question

How do you evaluate f(-2) given `f(x)=x^2-4`?

Answer 1

`0`

Explanation:

A function is a rule that tells you how you associate every input with its output.

This is what we mean when we write `y=f(x)`: we want to say that the `y` value depends on the `x` value, and the function `f` decides how this happen.

In your example, you have `y = x^2-4`, which means that whenever you choose an input `x`, you must square it (`x^2`) and subtract four (`x^2-4`) to get the output.

So, evaluating a function means exactly to do what I just said, but with a particular value chosen for `x`, in this case `-2`.

So, we only need to repeat the generic steps (square the input and subtract four), knowing that the input is `-2`.

When we square it we get `(-2)^2 = (-2)\times(-2) =4`, and when we subtract `4` we get `4-4=0`.

Once you get this concept, there is a faster way to evaluate functions: simply substitute the generic `x` value with the one you're interested in: we can rewrite the generic equation `x^2-4`, plugging `-2` where we see `x`. The equation becomes

`(-2)^2-4 = 4-4=0`