Question

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

$y=sec\left(\frac{2\mathrm{\pi }}{3}x\right)+2$

Short answer

graph of the function is

domain is $\left\{x\right|x\ne \pm \frac{3k}{4}\}$

range is$(-\infty ,1\}\cup \{3,\infty )$

Step-by-step solution

Step 1. The given information is

a function$y=sec\left(\frac{2\mathrm{\pi }}{3}x\right)+2$

Step 2. Making the parent graph we get,

Step 3. The graph of the given equation after stretching we get is,

Step 4. Domain and range

The graph of function state that the

The domain of the function is

the domain is $\left\{x\right|x\ne \pm \frac{3k}{4}\}$, where k is is an odd integer

and the range is$(-\infty ,1\}\cup \{3,\infty )$