Graphing Rational Functions Practice

1. Let $f(x)=\dfrac{2x^2-18}{g(x)}$, where $g(x)$ is a polynomial.

   Which of the following is a possible graph of $y=f(x)$?

   Dashed lines indicate asymptotes.

   1. 
   2. 
   3. 

   4. 

2. Let $f(x)=\dfrac{ax^n+bx^2+10}{cx^m+dx-2}$, where $m$ and $n$ are integers and $a$, $b$, $c$ and $d$ are unknown constants.

   Which of the following is a possible graph of $y=f(x)$?

   Dashed lines indicate asymptotes.

   1. 
   2. 
   3. 

   4. 

3. Let $f(x)=\dfrac{12x^5-b}{6x^5+cx-d}$, where $b$, $c$, and $d$ are unknown constants.

   Which of the following is a possible graph of $y=f(x)$?

   Dashed lines indicate asymptotes.

   1. 
   2. 
   3. 

   4. 

4. Let $f(x)=\dfrac{q(x)}{x^2+12x+36}$, where $q(x)$ is a polynomial.

   Which of the following is a possible graph of $y=f(x)$?

   Dashed lines indicate asymptotes.

   1. 
   2. 
   3. 
   4. 
      

Source: Khan Academy, https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:graphs-of-rational-functions/e/graphs-of-rational-functions
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