Question

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

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

Short answer

graph of the given function is

domain is $\left\{x\right|x\ne \pm k\mathrm{\pi }\}$

range is$(-\infty ,\infty )$

Step-by-step solution

Step 1. The given information is

a function$f\left(x\right)=2\left(\frac{1}{\tan \left(x\right)}\right)-1$

Step 2. Making the graph of 1/tanx 

Step 3. The graph of the given function after stretching it by 1 unit is

Step 4. Domain and range

The graph of function state that the

The domain of the function is

the domain is $\left\{x\right|x\ne \pm k\mathrm{\pi }\}$, k is an integer

range is$(-\infty ,\infty )$