Question

Please list what the tangent parent function.Can you make graph it scale both axes. With a short table of points+ domain and range. If there are asymptotes please identify and label.

Answer 1

First, use a calculator to create a table of values for the function:

`y=\tan (x)`

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

`((2k+1)\pi)/(2)+\pi k,k\in\Z`

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:

`x\in\R-\lbrace(2k+1)/(2)\pi|k\in\Z\rbrace`

he range is:

`y\in\R`

nd the asymptotes are:

`x=(2k+1)/(2)\pi,k\in\Z`