Chapter 6, Problem 54RE

To determine

Use the graph to determine domain and range of each function.

Answer to Problem 54RE

Domain of function: $4\tan \left(2x\right)=\left\{x\in R:\frac{2x}{\pi }+\frac{1}{2}\notin Z\right\}$

Range of function: $4\tan \left(2x\right)=\left(-\infty ,\infty \right)$

Explanation of Solution

Given information:

  $y=4\tan \left(2x\right)$

Graph of $y=4\tan \left(2x\right)$ :

  

The Domain of the given function is $\left\{x\in R:\frac{2x}{\pi }+\frac{1}{2}\notin Z\right\}$

As we can see from the above graph, it is continuous on every point, therefore the Range of graph will be all Real Numbers or $\left(-\infty ,\infty \right)$ .