The segment AB is a line joining the points A( -1 , -3) and B(3, 7).

The equation of the line joining them can be taken to be the function f(x).

The equation of the line is given by:

y + 3 = [( -3 - 7)/(-1 - 3)](x + 1)

=> y + 3 = (-10/-4)(x + 1)

=> y +3 = (5/2)(x + 1)

=> y = (5/2)(x + 1) - 3

=> y = (5x + 5 - 6)/2

=> y = (5x - 1)/2

Therefore **f(x) = (5x - 1)/2**