Question

Thomas is building rectangular boxes. The table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long.



Choose the function that represents the data.

f(x) = x2 + 2x

f(x) = 2x2
f(x) = 2x

Answer 1

I don’t see the table — could you paste the x and f(x) values?

Meanwhile, here’s how to decide from the three choices:

- If the other side of the rectangle is x + 2, area = x(x + 2) = x^2 + 2x. So f(x) = x^2 + 2x.
- If the other side is 2x, area = x(2x) = 2x^2. So f(x) = 2x^2.
- If the other side is a constant 2 ft, area = x·2 = 2x. So f(x) = 2x.

Quick numeric checks:
- Plug any one or two table entries into the three formulas and see which matches.
- Or check differences: if f values increase linearly (constant first differences) it’s 2x; if the second differences are constant = 2 it’s x^2+2x; if second differences are constant = 4 it’s 2x^2.

Send the table and I’ll pick (and show the work).