Question

How do you find the amplitude, period, vertical and phase shift and graph `y=5+tan(theta+pi/4)`?

Answer 1

As detailed.

Explanation:

`y = A tan (Bx - C) + D`

Given `y = tan (theta + pi/4) + 5`

`A = 1, B = 1, C = -pi/4, D = 5`

Amplitude `=` NONE for tangent function.

Period `pi / |B| = pi / 1 = pi`

Phase Shift `= -C / B = pi/4, pi/4` to the right.

Vertical Shift `= D = 5`

graph{tan (x + pi/4) + 5 [-10, 10, -5, 5]}