Identify and analyze discontinuities of rational functions

The  exercise appears under the Algebra II Math Mission. This exercise practices distinguishing between vertical asymptotes and removable discontinuities, and analyze a function's behavior around its vertical asymptotes.

Types of Problems
There is one types of problems in this exercise:


 * 1) Describe the behavior of the function $$q$$ around its vertical asymptote: This problem has an expression for the value of $$q(x)$$. The student is then expected to describe the behavior of the function $$q$$ around its vertical asymptote at a certain intgerIdentify and analyze discontinuities of rational functions.PNG

Strategies
Knowledge of determining end behaviors of rational functions is essential for success while doing this exercise.
 * 1) To find the behavior of $$q$$ as it approaches its asymptote from either direction, students need to first factor the expression. The zeros of the numerator and denominator will define intervals. Then, they can analyze the behavior at the intervals adjacent to the asymptote.
 * 2) Students should first factor the numerator and the denominator so they can find the input values that make them equal to 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.