Q. 26 - Precalculus Enhanced with Graphing Utilities

Question

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

$y=\frac{1}{2}csc x$

Step-by-Step Solution

Answer

The graph is

Domain is $\left\{x|x\ne \pm k\mathrm{\pi }, k is an integer\right\}$

Range is $(-\infty ,-\frac{1}{2}]\cup [\frac{1}{2},\infty )$

Step 1. Given information

We have been given the function as $y=\frac{1}{2}csc x$

Step 2. Draw the graph of the function.

The graph is

Step 3. Find the domain and range of the given function.

By looking at the graph,

Domain is $\left\{x|x\ne \pm k\mathrm{\pi }, k is an integer\right\}$

Range is $(-\infty ,-\frac{1}{2}]\cup [\frac{1}{2},\infty )$