End Behavior and Local Behavior of Rational Function Practice

1. Consider the following rational function $f$.

   $f(x)=\dfrac{-8x^4+3x^2-7x}{4x^2-4}$

   Determine $f$'s end behavior.

   $f(x)\to$  (-∞, -1/2, 0 , ∞) as $x\to -\infty$.

   $f(x)\to$  (-∞, -1/2, 0 , ∞) as $x\to \infty$.

2. Consider the following rational function $f$.

   $f(x)=\dfrac{-8x^3-3x+4}{2x^2-9}$

   Determine $f$'s end behavior.

   $f(x)\to$  (-∞, -1/2, 0 , ∞) as $x\to -\infty$.
   
   

   $f(x)\to$  (-∞, -1/2, 0 , ∞) as $x\to \infty$.

3. Consider the following rational function $f$.

   $f(x)=\dfrac{-8x^3+5x^2-1}{2x^3-9x}$

   Determine $f$'s end behavior.

   $f(x)\to$  (-∞, -1/2, 0 , ∞) as $x\to -\infty$.
   
   

   $f(x)\to$  (-∞, -1/2, 0 , ∞) as $x\to \infty$.

4. Consider the following rational function $f$.

   $f(x)=\dfrac{-4x^3+7x+9}{8x^6-9x^4-2x}$

   Determine $f$'s end behavior.

   $f(x)\to$  (-∞, -1/2, 0 , ∞) as $x\to -\infty$.
   
   $f(x)\to$  (-∞, -1/2, 0 , ∞) as $x\to \infty$.

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