Match graphs of rational functions to their formula

The  exercise appears under the Algebra II Math Mission. This exercise explores the graphs of rational functions and practices determining which of four graphs fits the formula of a given function.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find which of the following is a possible graph of the function: This problem provides the equation of the given rational function. The student is asked to find the graph that matches the function. Dashed lines indicate asymptotes.Match graphs of rational functions to their formula.PNG

Strategies
Knowledge of graphs of rational functions are encouraged to ensure success on this exercise.
 * 1) Vertical asymptotes occur when the denominator of a reduce rational expression is equal to zero.
 * 2) The horizontal asymptote is found by taking the limit of the equation as $$x$$ tends to infinity (or $$-\infty$$).
 * 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.

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.