# How do you graph y=-4cos(x/2) + 2?

Apr 19, 2016

Follow the explanation !

#### Explanation:

Note the crossing points (whenever the plot crosses x- or y- axis) )in all the following plots.

You know the plot of cos(x)
graph{cosx [-4.86, 5.14, -2.4, 2.6]}

Now, see calling x as $\frac{x '}{2}$ changes the x-coordinates only:

graph{cos(x/2) [-9.86, 10.14, -4.9, 5.1]}

as if you have renamed every point on the axis as their doubles. $x \to 2 x$

Now in the same way rename your y-axis point as the 4 times. $y \to 4 y$

graph{4cos(x/2) [-9.86, 10.14, -4.9, 5.1]}

Now take a mirror image of this plot with respect to x axis. $y \to - y$

graph{-4cos(x/2) [-12.66, 12.65, -6.59, 6.6]}

Now push everything up by 2. $y \to y + 2$

graph{2-4cos(x/2) [-12.66, 12.65, -6.59, 6.6]}