Question

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

Answer 1

Graphs are gifts, from the Socratic utility.

Explanation:

`y = tan^(-1)(2x-4)`

is inversely ( for the same graph but with restricted

`y in (-pi/2, pi/2)`)

`x=2 + (1/2) tan y`

Direct graph, using `y = arctan(2x-4)`:
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 +(1/2) tan y`, for `y in (-pi/2, pi/2)`. Of course, this includes

ranges `(-oo, oo)` for both x and y. Slide the cursor over the graph

`uarr` and `darr` to see the extended graph for (one x, many y)

plots, from the reverse inverse `y = kpi + tan^(-1)(2x-4)`, k =

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