Question

How do you graph `f(x)= 2+csc(2x+2)`?

Answer 1

As shown below:

Explanation:

The first thing we must consider is the transformations that `csc x` must undergo to reach `2+ csc(2x+2 )`

So first it must be translated by `(0,2)` or in other words, shifted upward by 2 units: yielding `2+ cscx`

Then stretched by a scale factor of `1/2` in the `x` direction:
yielding `2+csc(2x)`

Then translate by the vector `(-1,0)` to yield: `2+csc(2(x+1))`
`= 2+ csc(2x+2)`

`=>`

`cscx:` graph{cscx [-10, 10, -5, 5]}

`2+cscx`: graph{cscx + 2 [-9.71, 10.29, -2.32, 7.68]}

`2+csc2x` : graph{2+ csc(2x) [-9.71, 10.29, -2.32, 7.68]}

`2+csc(2x+2)`: graph{2+csc(2x+2) [-9.71, 10.29, -2.32, 7.68]}