# How do you shift and graph y=-3+sinx?

Oct 31, 2014

The period of $\sin$ is $2 \pi$.

The $- 3$ is applied to the result of $\sin \left(x\right)$ which affects the $y$ value.

All of the points will be shifted down $3$ units.

Rely on your knowledge of the unit circle to figure out the values of sin on the $x$ and $y$ axis.

$f \left(0\right) = - 3 + \sin \left(0\right) = - 3 + 0 = - 3 \to \left(0 , - 3\right)$

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

$f \left(\pi\right) = - 3 + \sin \left(\pi\right) = - 3 + 0 = - 3 \to \left(\pi , - 3\right)$

$f \left(\frac{3 \pi}{2}\right) = - 3 + \sin \left(\frac{3 \pi}{2}\right) = - 3 - 1 = - 4 \to \left(\frac{3 \pi}{2} , - 4\right)$

$f \left(2 \pi\right) = - 3 + \sin \left(2 \pi\right) = - 3 + 0 = - 3 \to \left(2 \pi , - 3\right)$

Enter the function into the calculator Set the interval, XMIN and MAX , from $\left[0 , 2 \pi\right] \to 2 \pi = 6.283185307$ Press the GRAPH button 