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 values? That will let me pick the correct formula.

Meanwhile, here’s how to decide from the numbers:

- If the bottom has sides x and (x + 2), area = x(x + 2) = x^2 + 2x.
- If the bottom has sides x and 2x, area = x·2x = 2x^2.
- If the bottom has sides x and 2, area = x·2 = 2x.

Quick numeric test you can do from the table: compute f(x)/x for any nonzero x.
- If f(x)/x equals 2 for all x, the formula is 2x.
- If f(x)/x equals x + 2 (i.e. varies as x + 2), the formula is x^2 + 2x.
- If f(x)/x equals 2x (i.e. equals 2 times x), the formula is 2x^2.

Send the table and I’ll pick the exact one.