Graphs of rational functions

The  exercise appears under the Algebra II Math Mission. This exercise explores the graphs of rational functions.

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


 * 1) Find the asymptotes from the equation: This problem provides a rational function with multiple asymptotes. The student is asked to find the asymptotes and write them in the spaces.Gorf1.png
 * 2) Match the equation with the graph: This problem has a collection of three graphs on a coordinate plane and three equations. The student is asked to match the equations with the correct graphs.Gorf2.png

Strategies
Knowledge of graphing, especially with asymptotes, and factoring are encouraged to ensure success on this exercise.
 * 1) Vertical asymptotes occur when the denominator of a reduce rational expression is equal to zero. The equations on this exercise do not reduce, so it is equivalent to just finding where the denominator is zero.
 * 2) The horizontal asymptote is found by taking the limit of the equation as x tends to infinity (or negative infinity).
 * 3) An alternative method to finding a horizontal asymptote is to plug a "large" number in for x in the equation.
 * 4) If the numerator and denominator have the same degree, the horizontal asymptote occurs at the ratio of the leading coefficients of the polynomials.
 * 5) On Match the equation with the graph it is recommended to locate vertical asymptotes first (where the denominator is zero). If this doesn't work, try finding the x-intercept (where the numerator is zero).

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.