Here are the essential concepts you must grasp in order to answer the question correctly.
Set-Builder Notation
Set-builder notation is a mathematical shorthand used to describe a set by specifying a property that its members must satisfy. For example, the interval [-3, 1] can be expressed in set-builder notation as {x | -3 ≤ x ≤ 1}, meaning 'the set of all x such that x is greater than or equal to -3 and less than or equal to 1.' This notation is particularly useful for defining intervals and sets in a concise manner.
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Intervals
An interval is a range of numbers between two endpoints, which can be open, closed, or half-open. A closed interval, like [-3, 1], includes its endpoints, meaning both -3 and 1 are part of the set. Understanding the types of intervals is crucial for accurately expressing them in set-builder notation and for graphing them on a number line.
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Graphing on a Number Line
Graphing an interval on a number line involves visually representing the range of values included in the interval. For the closed interval [-3, 1], you would draw a solid dot at -3 and 1 to indicate that these endpoints are included, and shade the region between them. This visual representation helps in understanding the extent of the interval and the values it encompasses.
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Graphing Lines in Slope-Intercept Form