Write a tangent function hx such that the halfway points on

Write a tangent function, h(x), such that the halfway points on one period are (- pi/2, -2) and (pi/2, 4)

period = 4*(pi/2) = 2pi

b = pi/2pi = 1/2

y = a*tan(bx) +d

(-pi/2 , -2) and (pi/2 , 4)

plug these points:

-2 = a*tan(-pi/4) +d

-2 = -a +d ------(1)

4 = a*tan(pi/4) +d

4 = a +d ------(2)

we get d = 1 ; a = 3

So, y = 3tan(x/2) +1