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

Jun 20, 2018

$0$

#### 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 $y = f \left(x\right)$: 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 ${\left(- 2\right)}^{2} = \left(- 2\right) \setminus \times \left(- 2\right) = 4$, 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

${\left(- 2\right)}^{2} - 4 = 4 - 4 = 0$