# How do you write an equation of the tangent function with period pi/4, phase shift pi, and vertical shift 1?

Jul 5, 2018

Equation is $y = \tan 4 \left(x + \pi\right) + 1$

#### Explanation:

Standard form of the tangent function is

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

Period $= \frac{\pi}{4} = \frac{\pi}{|} B |$

$| B | = \frac{\pi}{\frac{\pi}{4}} = 4$

Phase Shift $= - \frac{C}{B} = \pi$

$C = - B \cdot \pi = - 4 \cdot \pi = - 4 \pi$

Vertical Shift $= D = 1$

Equation is $y = \tan \left(4 x + 4 \pi\right) + 1$