Question

Choose the function that represents the data in the table.




f(x) = 2x – 3
f(x) = x2 – 3
f(x) = 2x2 – 3

Answer 1

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

Meanwhile, here is a quick way to decide which of those three fits:

- If the y-values change by the same amount when x increases by 1 (constant first differences), the function is linear. The common first difference equals the slope. If that common difference is 2, then f(x)=2x−3 is the match.

- If the first differences are not constant but the second differences are constant, the function is quadratic. For a quadratic f(x)=ax^2+bx+c, the constant second difference equals 2a. So:
- if the second difference = 2, then a = 1 → f(x)=x^2−3 (if c = f(0) = −3),
- if the second difference = 4, then a = 2 → f(x)=2x^2−3 (again check c = −3).

Also check f(0): if the table includes x=0, f(0) should equal −3 for any of these three.

If you paste the table I’ll apply these steps and pick the correct one.