Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(X-2) / {(X-1)(X-3)} = 0

Key Concepts

Rational Functions

A rational function is a function represented by the ratio of two polynomials. In this case, the function is given by 2(X-2) / {(X-1)(X-3)}, where the numerator is a linear polynomial and the denominator is a product of linear factors. Understanding the behavior of rational functions, including their asymptotes and intercepts, is crucial for solving equations and inequalities involving them.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed intervals) or excluded (open intervals). For example, (a, b) represents all numbers between a and b, not including a and b, while [a, b] includes both endpoints. This notation is essential for expressing the solution set of inequalities.

Graphical Interpretation of Inequalities

Graphical interpretation of inequalities involves analyzing the graph of a function to determine where it is greater than, less than, or equal to a certain value. In this case, the graph of the rational function helps identify the intervals where the function equals zero or is positive or negative. Understanding how to read and interpret these graphs is key to solving the given equation or inequality.