How do you evaluate #f(x)=1/2sin(πx+π)-3#?

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Answer 1 · 2018-06-24T09:43:55

As below.

#f(x) = (1/2) sin (pix + pi) - 3#

Standard form of sine function is #f(x0 = A sin (Bx - C) + D#

#A = 1/2, B = pi, C = -pi, D = -3#

#Amplitude = |A| = 1/2#

#"Period " = (2pi) / |B| = (2pi) / pi = 2#

#"Phase Shift " = -C / B = -pi / pi = -1, " 1 to the LEFT"#

#"Vertical Shift " = D = -3#

graph{(1/2) sin (pix + pi) - 3 [-10, 10, -5, 5]}