[tex]y=\tan (x-\pi)-2\text{ (option B)}[/tex]
Explanation:[tex]\begin{gathered} We\text{ have the following functions}\colon \\ y=\tan \mleft(x-\pi\mright)+2 \\ y=\tan \mleft(x-\pi\mright)-2 \\ y=\tan \mleft(x+2\mright)-\pi \\ y=\tan \mleft(2\mleft(x+\pi\mright)\mright)-2 \\ \\ \text{From the graph, we s}ee\text{ the line crosses the y ax i}s\text{ at y -= -2} \end{gathered}[/tex]
This means the only the function that has y intercept as -2 from the functions will e examined. As every other ones donot cross y axis at that point.
The functions with y-intercept as y = -2:
[tex]\begin{gathered} y=\tan \mleft(x-\pi\mright)-2 \\ y=\tan \mleft(2\mleft(x+\pi\mright)\mright)-2 \\ \\ We\text{ check of the function above have same graph given} \end{gathered}[/tex]
From the given graph:
[tex]\begin{gathered} \text{the line cuts the x ax is at x values }\frac{\pi}{2},\text{ }\frac{3\pi}{2},\text{ respectively before 4} \\ \frac{\pi}{2}=\text{ 1.5708} \\ \frac{3\pi}{2}\text{ = 4.7123} \\ \\ \text{The line cuts the x ax is of }y=\tan \mleft(2\mleft(x+\pi\mright)\mright)-2\text{ at 3 different places before }x\text{ = 4} \\ \text{The line cuts the x ax is of }y=\tan \mleft(x-\pi\mright)-2\text{ at 2 different places before }x\text{ = 4 } \\ \text{x = }1.107,\text{ 4.2}49 \end{gathered}[/tex][tex]\text{Hence, the correct function is }y=\tan \mleft(x-\pi\mright)-2\text{ (option B)}[/tex]
