Question

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

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

Short 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-by-step solution

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

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