Answer :
To have a constant rate of change, the function has to be a linear function of type y = mx+b.
The only function that has this form is f(x) = x/2+1, where the rate of change is m=1/2 and is constant for all values of x.
We can calculate the rate of change as:
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]If we replace f(x2) and f(x1) we get:
[tex]undefined[/tex]Answer: f(x) = x/2 + 1