Graph a function

Question

I have a question, I have a function:

$$f(x) = \frac{-x^2-10x}{2}$$

I'm really confused how to replace the x.

So, what would be the points in $y$ if $x$ were: $-4, -3, -2, -1, 0, 1, 2, 3, 4$?

Answer 1

The notation $f(x)$ means this is a function that accepts $x$ values. A function essentially is map that takes values from one set and maps them into another set, in this case from $x$ to $y$. The equal sign shows us what this function looks like and where the $x$'s are in the function. So $f(x)$ is actually how the function looks like when $x$ is plugged in. Now, for example we want to know what the value of this function is when $x = 0$ so we plug in $0$ into the function which is represented by this notation $f(0)$. Notice how we used parenthesis around the $x$ value that we plugged in; this is an important practice because it allows you to see what operations affect our plugged in $x$ value first.

$$ f(0) = \frac{-(0)^2 - 10(0)}{2} = 0 $$

Answer 2

This is a table of the $y$-values you're looking for.

As an example computation: when $x = -4$, we have $$ f(-4) = \frac{-(-4)^2 - 10(-4)}{2} = \frac{-16 + 40}{2} = \frac{24}{2} = 12 $$