How do you graph $y = \frac{1}{2} cos x + 3$ $y=1/2cosx+3$ ?

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Answer 1 · 2018-06-21T15:13:19

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

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

$y = a cos (b x - c) + d$ $y=acos(bx-c)+d$

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

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

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

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

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

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

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

How do you graph y=12cosx+3y=1/2cosx+3?