Determine the end behavior of rational functions

The  exercise appears under the Algebra II Math Mission. This exercise practices determining how a rational function behaves as x approaches $$+\infty$$ or $$-\infty$$.

Types of Problems
There are two types of problems in this exercise:


 * 1) Determine the end behavior as $$x$$ approaches ___: This problem has an expression for the value of $$f(x)$$.  The student is expected to find the value of $$f(x)$$ as $$x$$ approaches a certain value. Determine the end behavior of rational functions.PNG
 * 2) Find the horizontal/vertical asymptote of $$p(x)$$: This problem has an expression for the value of $$p(x)$$. The student is expected to find the horizontal/vertical asymptote of $$p(x)$$. The graph of $$p$$ may not have a horizontal/vertical asymptote.

Strategies
Knowledge of determining end behaviors of rational functions is essential for success while doing this exercise.
 * 1) When determining end behavior of a function, the only term that matters in the numerator and denominator is the variable term with the largest exponent.

Real-life Applications

 * 1) Rational functions are useful as examples of graphs that have many interesting features, such as asymptotes and non-obvious intervals of increasing and decreasing.