Q. 50 - Precalculus Enhanced with Graphing Utilities

Question

graph each function
$f\left(x\right)=\left\{\begin{array}{ll}csc x& 0<x<\mathrm{\pi }\\ 0& x=\mathrm{\pi }\\ cot c& \mathrm{\pi }<x<2\mathrm{\pi }\end{array}\right.$

Step-by-Step Solution

Answer

The graph of$f\left(x\right)=\left\{\begin{array}{ll}csc x& 0<x<\mathrm{\pi }\\ 0& x=\mathrm{\pi }\\ cot c& \mathrm{\pi }<x<2\mathrm{\pi }\end{array}\right.$ is 

Step 1. Given data

The given function is

$f\left(x\right)=\left\{\begin{array}{ll}csc x& 0<x<\mathrm{\pi }\\ 0& x=\mathrm{\pi }\\ cot c& \mathrm{\pi }<x<2\mathrm{\pi }\end{array}\right.$

Step 2. Points of f ( x ) = c s c &#160; x

Consider different values of x from$(0,\infty )$ for$f\left(x\right)=csc x$  and determine several coordinates of points 

Step 3. Points of

Consider different values of x from $(\mathrm{\pi },2\mathrm{\pi })$for$f\left(x\right)=cot x$ and determine several coordinates of points 

Step 4. Graph of the function

Use the coordinates of points and Plot the graph of $f\left(x\right)=\left\{\begin{array}{ll}csc x& 0<x<\mathrm{\pi }\\ 0& x=\mathrm{\pi }\\ cot c& \mathrm{\pi }<x<2\mathrm{\pi }\end{array}\right.$