Which of the following rules could represent the function shown in the table?
x y
-1 -1
0 1
1 3

f(x) = -2x (a)

f(x) = 2x - 1 (b)

f(x) = 2x + 1 (c)

ANSWER

The rule is given by the relation,



EXPLANATION

We need to check and see if there is a constant difference between the y-values.



We can see that, there is a constant difference of 2.

This means that the table represents a linear relationship.

Let the rule be of the form,


Then the points in the table should satisfy the above rule.

So let us plug in



This implies that,







Our rule now becomes,



We again plug in another point say, (-1,-1) in to equation (1) to get,



we solve for m now to obtain,






We now substitute back in to equation (1) to get