Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Functions
A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. In this case, the function is 7x(x - 1)(x - 2), which is a cubic polynomial. Understanding the behavior of polynomial functions, including their roots and end behavior, is crucial for solving inequalities involving them.
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Inequalities and Interval Notation
Inequalities express a relationship where one side is not equal to the other, often using symbols like '>' or '<'. Interval notation is a way to represent the solution set of an inequality, indicating the range of values that satisfy the condition. For example, the solution to the inequality 7x(x - 1)(x - 2) > 0 can be expressed in interval notation to show where the function is positive.
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Graph Interpretation
Interpreting graphs involves analyzing the visual representation of functions to understand their behavior, such as where they are above or below the x-axis. In this case, the graph of 7x(x - 1)(x - 2) helps identify the intervals where the function is greater than zero, which is essential for solving the given inequality. Recognizing key features like intercepts and turning points is vital for this analysis.
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