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

Jun 24, 2018

As below.

#### Explanation:

$f \left(x\right) = \left(\frac{1}{2}\right) \sin \left(\pi x + \pi\right) - 3$

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

$A = \frac{1}{2} , B = \pi , C = - \pi , D = - 3$

$A m p l i t u \mathrm{de} = | A | = \frac{1}{2}$

$\text{Period } = \frac{2 \pi}{|} B | = \frac{2 \pi}{\pi} = 2$

$\text{Phase Shift " = -C / B = -pi / pi = -1, " 1 to the LEFT}$

$\text{Vertical Shift } = D = - 3$

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