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

Jun 17, 2018

As detailed.

#### Explanation:

$y = A \tan \left(B x - C\right) + D$

Given $y = \tan \left(\theta + \frac{\pi}{4}\right) + 5$

$A = 1 , B = 1 , C = - \frac{\pi}{4} , D = 5$

Amplitude $=$ NONE for tangent function.

Period $\frac{\pi}{|} B | = \frac{\pi}{1} = \pi$

Phase Shift $= - \frac{C}{B} = \frac{\pi}{4} , \frac{\pi}{4}$ to the right.

Vertical Shift $= D = 5$

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