At a summer camp, one large tub of mayonnaise is used for each lunch service. The function below represents the amount of mayonnaise, in tablespoons, left in the tub after N students are served lunch.

M(N) = 4000 - 4N

What is the domain of M(N)?

Question

At a summer camp, one large tub of mayonnaise is used for each lunch service. The function below represents the amount of mayonnaise, in tablespoons, left in the tub after N students are served lunch.

M(N) = 4000 - 4N

What is the domain of M(N)?

Extrinix · Answer

So to solve for $\sf{N}$, we can remove $\sf{M(N)}$ and make it into $\sf{0}$.

$\sf{0=4000-4N}$

Simply solve for $\sf{N}$.

$\sf{0=4000-4N}$        Subtract 4000 from each side.

$\sf{-4000=-4N}$         Divide both sides by -4.

$\sf{\dfrac{-4000}{-4}=N}$             Simplify it.

$\sf{1000=N}$                  And you have what N is!

Now, that given, you have to find the domain.

This can be done by simply finding 2 points along the line that can represent the graph (in this case, we start with 4000 tablespoons at 0 students and go down by 4 per each student.

Let's use the easiest one we can do, (1000,0), the amount of mayonnaise left in the jars.

Given these two points:
(0,4000) , (1000,0)
we can find both interval notation AND inequality notation.

Interval notation: $\sf{[0, 1000]}$
- Both sides are closed (hence the brackets []), which mean that the numbers 0 and 1000 are included

Inequality notation: $\sf{0 \le x \le 1000}$
- Both sides are closed (hence the $\sf{\le}$ symbol, which means the same as interval notation. "Zero is less than or equal to x which is less than or equal to 1000."

That's as in-depth as I can currently explain it considering it's 03:00.

Best of luck,
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