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

Dec 10, 2017

As shown below:

#### Explanation:

The first thing we must consider is the transformations that $\csc x$ must undergo to reach $2 + \csc \left(2 x + 2\right)$

So first it must be translated by $\left(0 , 2\right)$ or in other words, shifted upward by 2 units: yielding $2 + \csc x$

Then stretched by a scale factor of $\frac{1}{2}$ in the $x$ direction:
yielding $2 + \csc \left(2 x\right)$

Then translate by the vector $\left(- 1 , 0\right)$ to yield: $2 + \csc \left(2 \left(x + 1\right)\right)$
$= 2 + \csc \left(2 x + 2\right)$

$\implies$

$\csc x :$ graph{cscx [-10, 10, -5, 5]}

$2 + \csc x$: graph{cscx + 2 [-9.71, 10.29, -2.32, 7.68]}

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

$2 + \csc \left(2 x + 2\right)$: graph{2+csc(2x+2) [-9.71, 10.29, -2.32, 7.68]}