# How do you graph y=5+sin(1/2x)?

Jun 7, 2018

The graph will be a sine function centered on $y = 5$ with a period of $4 \pi$

#### Explanation:

$y = 5 + \sin \left(\frac{1}{2} x\right)$

$y = \sin \left(\frac{1}{2} x\right) + 5$

Standard Form is:

y=asin(bx-c) + d

a=amplitude or vertical stretch/compression
b=horizontal stretch/compression
c=horizontal shift
d=vertical shift

Your function $b = \frac{1}{2}$ and $d = 5$:

a horizontal stretch by a factor of 2 will make the period $4 \pi$.

a vertical shift up 5 units.

The graph will be a sine function centered on $y = 5$ with a period of $4 \pi$

graph{sin(1/2x) +5 [-11.58, 8.42, 0.68, 10.68]}