# How do you graph y=tan^-1(2x-4) over the interval -2<=x<=6?

Feb 3, 2017

Graphs are gifts, from the Socratic utility.

#### Explanation:

$y = {\tan}^{- 1} \left(2 x - 4\right)$

is inversely ( for the same graph but with restricted

$y \in \left(- \frac{\pi}{2} , \frac{\pi}{2}\right)$)

$x = 2 + \left(\frac{1}{2}\right) \tan y$

Direct graph, using $y = \arctan \left(2 x - 4\right)$:
graph{(y-arctan(2x-4))(y+1.573+.01x)(y-1.573+.01x)=0 [-2 6 -1.8 1.8]}

Same graph, using the inverse

$x = 2 + \left(\frac{1}{2}\right) \tan y$, for $y \in \left(- \frac{\pi}{2} , \frac{\pi}{2}\right)$. Of course, this includes

ranges $\left(- \infty , \infty\right)$ for both x and y. Slide the cursor over the graph

$\uparrow$ and $\downarrow$ to see the extended graph for (one x, many y)

plots, from the reverse inverse $y = k \pi + {\tan}^{- 1} \left(2 x - 4\right)$, k =

integer.
graph{(x-2-0.5 tan y )(y+1.573+.01x)(y-1.573+.01x)=0 [-2 6 -1.8 1.8]}