Function, Input and Output

Question

1. Identify the function that has the following input and output values:

Input (x)	1	2	3
Output f(x)	2	5	10

Answer 1

y=(x^2) + 1 works but there could be many other answers

Answer 2

f(1) = 2

f(2) = 5

f(3) = 10

We can see that the function seems to be increasing at a greater rate as x increases, so this is not a linear function, and there is likely some sort of exponent involved. We can see that x^2 < f(x) < x^3 for the given inputs and outputs.

The most straightforward function that would fit the given info is:

f(x) = x^2 + 1