Question

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

Answer 1

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 `(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-> 2x`

Now in the same way rename your y-axis point as the 4 times. `y->4y`

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->-y`

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

Now push everything up by 2. `y->y+2`

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