Question

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

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

Short answer

The graph of the equation

The domain is $\left\{x\right|x\ne \pm \frac{2k}{3}\}$

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

Step-by-step solution

Step 1. The given information is

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

Step 2. The graph of the parent equation is

Step 3. The graph of the equation we get is

Step 4. Domain and range is

The graph of function state that the

The domain of the function is

the domain is $\left\{x\right|x\ne \pm \frac{2k}{3}\}$

The range is$(-\infty ,-1]\cup [1,\infty )$