Question

Please help with his calc equation.

Write an equation of the tangent function with period pi/4, phase shift pi, and vertical shift 1.

Answer 1

tan(x) has a period of pi.
tan(ax) has a period of pi/a
So to have a period of pi/4, pi/a = pi/4. So a = 4
tan(4x) has a period of pi/4
Phase shift of pi units to the right means, subtract pi from x.
tan(4(x - pi))
vertical shift of + 1 means add 1 to the function.
So the function f(x) = tan(4x - 4pi) + 1

Answer 2

And since tan repeats itself every pi radians, subtracting the 4pi will have no effect and therefore can be taken out. tan(4x - 4pi) + 1 = tan(4x) + 1