# How do you graph and list the amplitude, period, phase shift for y=-sin(pi/4(x+1))+1?

Mar 18, 2018

As below.

#### Explanation:

Standard form of equation is $y = a \sin \left(b x - c\right) + d$

Given : $y = - \sin \left(\left(\frac{\pi}{4}\right) x + \frac{\pi}{4}\right) + 1$

$\text{Amplitude } = | a | = 1$

$\text{Period } = p = \frac{2 \pi}{|} b | = \frac{2 \pi}{\frac{\pi}{4}} = 8 \pi$

$\text{Phase Shift } = - \frac{\frac{\pi}{4}}{\frac{\pi}{4}} = 1$ $\textcolor{w h i t e}{a a a} \left(\text{1 to the left}\right)$

$\text{Vertical Shift} = d = 1$

graph{-sin((pi/4)x + (pi/4)) + 1 [-10, 10, -5, 5]}