Question

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

Answer 1

As below.

Explanation:

Standard form of equation is `y = a sin(bx - c) + d`

Given : `y = - sin ((pi/4)x + pi/4) + 1`

`"Amplitude " = |a| = 1`

`"Period " = p = (2pi) / |b| = (2pi) / (pi/4) = 8pi`

`"Phase Shift " = -(pi/4) / (pi/4) = 1` `color(white)(aaa)("1 to the left")`

`"Vertical Shift" = d = 1`

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