Q. 22 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 17– 40, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. 

$y= \tan \left(\frac{1}{2}x\right)$

Step-by-Step Solution

Answer

The graph is

The domain of the function is $\left\{\mathrm{x}|\mathrm{x}\ne \pm k\mathrm{\pi }, \mathrm{k} \mathrm{is} \mathrm{an} \mathrm{odd} \mathrm{integer}\right\}.$

The range of the function is a set of all real numbers or $\left(-\infty ,\infty \right).$

Step 1. Given Information

The given function is $y=\tan \left(\frac{1}{2}x\right).$

We have to graph the function and by using the graph determine the domain and the range of the function.

Step 2. Sketch the graph of the function

Step 3. Determining the domain and range of the function

By using the graph, the domain of the function is $\left\{\mathrm{x}|\mathrm{x}\ne \pm k\mathrm{\pi }, \mathrm{k} \mathrm{is} \mathrm{an} \mathrm{odd} \mathrm{integer}\right\}.$

The range of the function is the set of all real numbers or $\left(-\infty ,\infty \right).$