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Interval

from class:

Algebra and Trigonometry

Definition

An interval is a range of numbers between two given values. It can be either closed, open, or half-open depending on whether the endpoints are included.

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5 Must Know Facts For Your Next Test

  1. A closed interval $[a, b]$ includes both endpoints: $a$ and $b$.
  2. An open interval $(a, b)$ excludes both endpoints: $a$ and $b$.
  3. A half-open (or half-closed) interval can include one endpoint but not the other, such as $[a, b)$ or $(a, b]$.
  4. Intervals are often used to express solutions to inequalities.
  5. Graphically, intervals can be represented on a number line with solid dots for included endpoints and open circles for excluded ones.

Review Questions

  • What is the difference between a closed interval and an open interval?
  • How would you graphically represent the interval $(2, 5]$?
  • If you have the inequality $3 < x \leq 7$, how would you write this as an interval?
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