Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Functions
A rational function is a function that can be expressed as the ratio of two polynomials. In this case, the function is given by 2(X-2) / {(X-1)(X-3)}, where the numerator and denominator are both polynomials. Understanding the behavior of rational functions, including their asymptotes and intercepts, is crucial for analyzing their graphs and solving inequalities.
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Intro to Rational Functions
Inequalities and Interval Notation
Inequalities express a relationship where one side is not equal to the other, often indicating a range of values. Interval notation is a way to represent these ranges succinctly, using parentheses and brackets to denote whether endpoints are included or excluded. For example, the interval (a, b) includes all numbers between a and b but not a and b themselves, while [a, b] includes a and b.
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Graphing and Analyzing Functions
Graphing functions involves plotting points on a coordinate plane to visualize their behavior. Analyzing the graph helps identify key features such as intercepts, asymptotes, and regions where the function is positive or negative. In the context of the given inequality, understanding how to interpret the graph will aid in determining the solution set where the function is less than zero.
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Graphs of Logarithmic Functions