Q. 37 - Precalculus Enhanced with Graphing Utilities

Question

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

$y=\frac{1}{2}\tan \left(\frac{1}{4}x\right)-2$

Step-by-Step Solution

Answer

graph of the given function is

the domain is $\left\{x\right|x\ne \pm 2k\mathrm{\pi }\}$

the range is $(-\infty ,\infty )$

Step 1. The given information is

a function $f\left(x\right)=\frac{1}{2}\tan \left(\frac{1}{4}x\right)-2$

Step 2. Making the parent graph we get,

$y=\tan x$

Step 3. Making the graph of the given function we get,

$y=\frac{1}{2}\tan \left(\frac{1}{4}x\right)-2$

Step 4. Domain and range is

The graph of function state that the

The domain of the function is

the domain is $\left\{x\right|x\ne \pm 2k\mathrm{\pi }\}$, k is an odd integer

the range is $(-\infty ,\infty )$