# How do you graph y=1/2cosx+3?

Jun 21, 2018

your graph is moved up vertically 3 units and its amplitude is cut in half as compared to the parent function $y = \cos x$

#### Explanation:

Use this standard formula to convert from the parent function $y = \cos x$

$y = a \cos \left(b x - c\right) + d$

a = amplitude
b = horizontal stretch
c = horizontal shift
d = vertical shift

your function has a amplitude of $\frac{1}{2}$ and a vertical shift of $+ 3$

$y = \cos x$ has a amplitude of 1 and no shift:

graph{cosx [-10, 10, -5, 5]}

$y = \frac{1}{2} \cos x + 3$

So your graph is moved up vertically 3 units and its amplitude is cut in half:

graph{1/2cosx + 3 [-10, 10, -5, 5]}