Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They use symbols such as ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than). Understanding how to interpret and graph inequalities is essential for visualizing the solution set of an inequality on a coordinate plane.
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Logarithmic Functions
Logarithmic functions are the inverses of exponential functions and are defined as y = log_b(x) if and only if b^y = x, where b is the base. In the given inequality, log(x - 1) indicates a logarithmic function with a domain restriction (x > 1). Understanding the properties of logarithms, including their domain and range, is crucial for accurately graphing the inequality.
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Graphs of Logarithmic Functions
Graphing Techniques
Graphing techniques involve plotting points on a coordinate plane to represent equations or inequalities visually. For inequalities, the graph typically includes a boundary line (or curve) and shading to indicate the solution set. Knowing how to determine whether to use a solid or dashed line, as well as how to shade the appropriate region, is vital for correctly representing the solution to the inequality.
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Graphs and Coordinates - Example