Question

How do you graph `5+8cos2x`?

Answer 1

We have `f(x) = 5 + 8cos2x`

Let's first breakdown the above equation.
`cosx` is pretty simple to plot as a function of x (just a sinusoidal wave). Now, `cos2x` plot looks exactly same as `cosx` but it varies two times faster than `cosx` (see the plots below).

`cosx`

graph{cos(x) [-10, 10, -2, 2]}

`cos2x`

graph{cos(2*x) [-10, 10, -2, 2]}

Multiplying `cos2x` by `8` gives you the following plot
(changes the amplitude of the curve)
`8cos2x`

graph{8cos(2x) [-10, 10, -10, 10]}

Finally, adding `5` to `8cos2x` shifts the plot by 5 on the y-axis
`5+8cos2x`

graph{5+8cos(2x) [-10, 10, -6, 14]}