Question

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

Answer 1

As below.

Explanation:

`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]}