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). h(x)=______________

y=a tan(b(x-h))+k

a=period ; a = (4-(-2))/2 = 3
b=period ; b = pi
h=horizontal shift
k=midline ; k = 1

y = 3tan(x+h) +1

we would find phase shift using one point ( pi/2 , 2)

4 = 3tan(pi/2 +h) +1

tan(pi/2 +h)= 1

pi/2 +h = pi/4

h= -pi/4

So, y = 3tan(x -pi/4) +1

So, h(x) = 3tan(x -pi/4) +1