Q. 49 - Precalculus Enhanced with Graphing Utilities

Question

graph each function

$f\left(x\right)=\left\{\begin{array}{ll}\tan x& 0\le x<\frac{\mathrm{\pi }}{2}\\ 0& x=\frac{\mathrm{\pi }}{2}\\ sec c& \frac{\mathrm{\pi }}{2}<x\le \mathrm{\pi }\end{array}\right.$

Step-by-Step Solution

Answer

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

Step 1. Given data

The given function is

$f\left(x\right)=\left\{\begin{array}{ll}\tan x& 0\le x<\frac{\mathrm{\pi }}{2}\\ 0& x=\frac{\mathrm{\pi }}{2}\\ sec c& \frac{\mathrm{\pi }}{2}<x\le \mathrm{\pi }\end{array}\right.$

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

Consider different values of x from$[0,\frac{\mathrm{\pi }}{2})$ for $f\left(x\right)=\tan x$ and determine several coordinates of points

Step 3. Points of f ( x ) = s e c &#160; x

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

Step 4. Graph of the function

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