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An open-top box is created by cutting squares out of corners of an 8.5-inch by 11-inch sheet of paper and then folding up the sides.

sheet of paper with square corner cut-outs

[Click image to enlarge]

They ask me to define a function $f$ to determine the volume of the box (measured in cubic inches) in terms of the length $x$ of the side of the square cutout (in inches), and I am not really sure what they are asking me to do here.

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    Start by drawing a diagram and looking at it. – 2017-02-09
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    I added an image, to illustrate what the problem is about. It is fairly straightforward to come up with the formula for $f$, the volume of the open-top box. – 2017-02-10

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Calculating the volume, $f:length⋅width⋅heigth$.

Since you are cutting out squares you only need one variable, $x$. Your lengt will be $8,5-x-x $ since you are cutting out squares at both ends. Your width $11-x-x$. And the heigth $x$ since you are folding the squares up.

So your function $f$ of your volume will be $f(x)=(8,5-2x)⋅(11-2x)⋅x$

=$f(x)=4x^3-39x^2+93,5x$

only don't forget to convert the inches to cm

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    Why the nonsense about centimetres? It could be cubits or furlongs, the maths is the same. Are you just trying to confuse the OP? – 2017-02-10
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    in his discription he said he wanted the volume in cubic centimeters, and he gave the discription of the sheet of paper in inches so you need to convert them right? – 2017-02-10
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    I've looked through the edit history and I can't see anything about centimetres. – 2017-02-10