Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Inequalities
Polynomial inequalities involve expressions that compare a polynomial to a value, typically zero, using inequality symbols such as ≥, ≤, >, or <. To solve these inequalities, one must determine the intervals where the polynomial is either above or below the specified value. This often requires finding the roots of the polynomial and testing intervals between these roots.
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Graphing on a Number Line
Graphing the solution set of a polynomial inequality on a number line visually represents the intervals where the inequality holds true. Solutions are typically marked with open or closed circles to indicate whether endpoints are included (closed) or excluded (open). This graphical representation helps in understanding the range of values that satisfy the inequality.
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Graphing Lines in Slope-Intercept Form
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 or excluded. For example, (a, b) means all numbers between a and b, excluding a and b, while [a, b] includes both endpoints. This notation is essential for clearly expressing the solution set of inequalities.
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