Q. 22 - Calculus

Question

Find the equation of a rational function that could have the graph shown. Take into account roots, holes, and vertical and horizontal asymptotes when constructing your function. 

  

Step-by-Step Solution

Answer

Ans:  $\left(\mathrm{x}\right)=\left\{\begin{array}{l}\frac{x}{1-x^2}:-1<x<1\\ \frac{2x}{1-x^2}+2:x>1\\ \frac{2x}{1-x^2}+2:x<-1\end{array}\right.$

Step 1. Given information.

given,

  the rational function that could have the graph given in the question.

Step 2. The function would be

 $\left(\mathrm{x}\right)=\left\{\begin{array}{l}\frac{x}{1-x^2}:-1<x<1\\ \frac{2x}{1-x^2}+2:x>1\\ \frac{2x}{1-x^2}+2:x<-1\end{array}\right.$

Step 3. Now the graph of the function is given below