Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Functions
A rational function is a function represented by the ratio of two polynomials. It is typically expressed in the form f(x) = P(x)/Q(x), where P and Q are polynomials. Understanding the behavior of rational functions is crucial for analyzing their graphs, particularly in identifying asymptotic behavior and intercepts.
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Asymptotes
Asymptotes are lines that the graph of a function approaches but never touches. There are two main types: vertical asymptotes, which occur where the function is undefined (typically where the denominator is zero), and horizontal asymptotes, which describe the behavior of the function as x approaches infinity or negative infinity. These concepts help in predicting the end behavior of rational functions.
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Limits
Limits are fundamental in calculus and are used to describe the behavior of functions as they approach a certain point. In the context of rational functions, limits help determine the value that f(x) approaches as x approaches a specific value, such as -2 from the right (denoted as -2^+). This is essential for understanding the function's behavior near vertical asymptotes.
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