Question

Choose the function that represents the data in the table.

x 0 1 2 3 4 5
f(x) -3 -1 1 3 5 7

A. f(x)= 2/x-3
B. f(x)= 2x-3
C. f(x)= x^2-3
D. f(x)= 2x^2-3

Answer 1

B. f(x) = 2x-3

Explanation:

The first point in the table tells you there will be an added constant of -3. All answer choices agree on this.

The x-values are evenly spaced, so we can examine the f(x) values to see what sort of function it is. It usually works well to consider the differences of adjacent values. Here, we see they are ...

-1 -(-3) = 2

1 -(-1) = 2

3 -1 = 2

5 -3 = 2

7 -5 = 2

All of the differences are the same value, 2, so this is a linear function. There is only one answer choice that is a linear function:

f(x) = 2x -3