Here are the essential concepts you must grasp in order to answer the question correctly.
Interval Notation
Interval notation is a mathematical notation used to represent a range of numbers. It uses parentheses and brackets to indicate whether endpoints are included or excluded. For example, (1, 6] means that 1 is not included in the interval, while 6 is included. This notation is essential for understanding the boundaries of the interval.
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Set-Builder Notation
Set-builder notation is a concise way to express a set by specifying a property that its members must satisfy. For the interval (1, 6], it can be expressed as {x | 1 < x ≤ 6}, meaning 'the set of all x such that x is greater than 1 and less than or equal to 6.' This notation is useful for defining intervals in a more formal mathematical context.
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Graphing Intervals on a Number Line
Graphing intervals on a number line visually represents the range of values included in the interval. For (1, 6], you would draw an open circle at 1 (indicating it is not included) and a closed circle at 6 (indicating it is included), then shade the region between them. This graphical representation helps in understanding the interval's limits and the values it encompasses.
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Graphing Lines in Slope-Intercept Form