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

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Answer 1 · 2018-03-18T10:44:37

As below.

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]}