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

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Answer 1 · 2017-12-10T11:36:23

As shown below:

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

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

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

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

$\Rightarrow$ $=>$

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

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

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

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

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