Question

Choose the function whose graph is given by: -3 -2 1 39 2 쪽 35 - 2 / 2 1 2 2 3 O A. y = tan(x - 2) + 2 O - B. y = tan(x - ) - 2 O c. y = tan(x + 2) - 1 D. y = tan(2(x + 7)) - 2

Answer 1

`y=\tan (x-\pi)-2\text{ (option B)}`

Step-by-step explanation:
`\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}`

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:

`\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}`

From the given graph:

`\begin{gathered} \text{the line cuts the x ax is at x values }(\pi)/(2),\text{ }(3\pi)/(2),\text{ respectively before 4} \\ (\pi)/(2)=\text{ 1.5708} \\ (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}`
`\text{Hence, the correct function is }y=\tan \mleft(x-\pi\mright)-2\text{ (option B)}`