Function A has a slope of (4-(-2))/(4-(-4)) = 6/8 = 3/4, Function B has a slope of 2/5, so any function with a slope between those values will be satisfactory. We know the value 1/2 is between 2/5 and 3/4, so we can make our function have a slope of 1/2.
If we choose a y-intercept of 17/7, then our function will intersect the other two where they already intersect each other. That makes the graph clearly show the rate of change is between the rates of change of the given functions.
A third function that satisfies requirements will be
.. f(x) = (1/2)x +17/7
