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)= x^2/2
f(x) = 2x2
f(x) = 2x

Answer 1

I don't see the table you mention — I need the actual x and f(x) values to pick the right function. Can you paste the table?

How to decide (so you can check quickly): the bottom area = x × (the other side). So compute f(x)/x for the table values:

- If f(x)/x = x + 2 (depends on x) then f(x) = x(x+2) = x^2 + 2x.
- If f(x)/x = x/2 then f(x) = x(x/2) = x^2/2.
- If f(x)/x = 2x then f(x) = x(2x) = 2x^2.
- If f(x)/x = 2 (constant) then f(x) = x(2) = 2x.

Example checks:
- If f(1)=3, f(2)=8, f(3)=15 → f(x)=x^2+2x.
- If f(1)=2, f(2)=4, f(3)=6 → f(x)=2x.
- If f(1)=0.5, f(2)=2, f(3)=4.5 → f(x)=x^2/2.
- If f(1)=2, f(2)=8, f(3)=18 → f(x)=2x^2.

Send the table and I'll pick the correct function.