Question

graph each function

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

Short answer

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

Step-by-step solution

Step 1. Given data

The given function is

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

Step 2. Points of f(x)=tan 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)=sec x

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

Step 4. Graph of the function 

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