Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 109

Capitolo 2, Problema 109

In Exercises 107–110, use graphs to find each set. [1,3) ∩ (0,4)

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Step 1: Understand the notation. The interval [1,3) means all numbers from 1 to 3, including 1 but not including 3. The interval (0,4) means all numbers greater than 0 and less than 4, excluding both 0 and 4.

Step 2: Represent each interval on a number line. For [1,3), draw a solid dot at 1 (to indicate inclusion) and an open circle at 3 (to indicate exclusion). For (0,4), draw open circles at both 0 and 4.

Step 3: Identify the intersection ∩ of the two intervals. The intersection represents the set of numbers that are common to both intervals.

Step 4: On the number line, observe where the two intervals overlap. The overlap starts at 1 (included because of [1,3)) and ends at 3 (excluded because of [1,3)).

Step 5: Write the result of the intersection as an interval. The intersection is [1,3), which includes all numbers from 1 to 3, including 1 but not including 3.

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Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses brackets and parentheses to indicate whether endpoints are included or excluded. For example, [1, 3) means that 1 is included in the interval, while 3 is not, indicating all numbers from 1 up to but not including 3.

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Interval Notation

Set Intersection

Set intersection refers to the operation of finding common elements between two sets. The intersection of sets A and B, denoted as A ∩ B, includes only those elements that are present in both sets. In the context of intervals, this means identifying the overlapping range of values that satisfy both conditions.

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Parallel & Perpendicular Lines

Graphing Intervals

Graphing intervals involves visually representing the range of values on a number line. Each interval is depicted with a line segment, where closed intervals are marked with solid dots and open intervals with open dots. This visual representation helps in easily identifying overlaps and intersections between different intervals.

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Identifying Intervals of Unknown Behavior

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