First, use a calculator to create a table of values for the function:
[tex]y=\tan (x)[/tex]
A table with inputs for x starting at -6.5 reaching the value of 6.5 with steps of 0.5 would be:
Plotting all the points and joining them with a smooth line, we can see that the graph of y=tan(x) is:
As we can see from the graph, the curve has an asymptote at
[tex]\frac{(2k+1)\pi}{2}+\pi k,k\in\Z[/tex]
On the other hand, the graph reaches all the real values over the Y-axis. Then, the range of the function is the set of all real numbers.
herefore, the domain is:
[tex]x\in\R-\lbrace\frac{2k+1}{2}\pi|k\in\Z\rbrace[/tex]
he range is:
[tex]y\in\R[/tex]
nd the asymptotes are:
[tex]x=\frac{2k+1}{2}\pi,k\in\Z[/tex]
