Q. 36 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

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 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 $(-\infty ,-1]\cup [1,\infty )$