Q. 34 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

graph of the given function is

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

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

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 / tan x

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 $(-\infty ,\infty )$