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Domain and Interval Notation

Domain and Interval Notation. Domain. The set of all possible input values (generally x values) We write the domain in interval notation Interval notation has 2 important components: Position Symbols. Interval Notation – Position. Has 2 positions: the lower bound and the upper bound

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Domain and Interval Notation

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  1. Domain and Interval Notation

  2. Domain • The set of all possible input values (generally x values) • We write the domain in interval notation • Interval notation has 2 important components: • Position • Symbols

  3. Interval Notation – Position • Has 2 positions: the lower bound and the upper bound [4, 12) • Lower Bound • 1st Number • Lowest Possible x-value • Upper Bound • 2nd Number • Highest Possible x-value

  4. [ ] → brackets Inclusive (the number is included) =, ≤, ≥ ● (closed circle) ( ) → parentheses Exclusive (the number is excluded) ≠, <, > ○ (open circle) Interval Notation – Symbols • Has 2 types of symbols: brackets and parentheses [4, 12)

  5. Understanding Interval Notation 4 ≤ x < 12 • Interval Notation: • How We Say It: The domain is 4 to 12 . • On a Number Line:

  6. Example – Domain: –2 < x ≤ 6 • Interval Notation: • How We Say It:The domain is –2 to 6 . • On a Number Line:

  7. Example – Domain: –16 < x < –8 • Interval Notation: • How We Say It:The domain is –16 to –8 . • On a Number Line:

  8. Your Turn: • Complete problems 1 – 3 on the “Domain and Interval Notation – Guided Notes” handout

  9. Infinity • Infinity is always exclusive!!! • – The symbol for infinity

  10. Infinity, cont. Negative Infinity Positive Infinity

  11. Example – Domain: x ≥ 4 • Interval Notation: • How We Say It:The domain is 4 to • On a Number Line:

  12. all real numbers Example – Domain: x is • Interval Notation: • How We Say It:The domain is to • On a Number Line:

  13. Your Turn: • Complete problems 4 – 6 on the “Domain and Interval Notation – Guided Notes” handout

  14. Restricted Domain • When the domain is anything besides (–∞, ∞) • Examples: • 3 < x • 5 ≤ x < 20 • –7 ≠ x

  15. Combining Restricted Domains • When we have more than one domain restriction, then we need to figure out the interval notation that satisfies all the restrictions • Examples: • x ≥ 4, x ≠ 11 • –10 ≤ x < 14, x ≠ 0

  16. Combining Multiple Domain Restrictions, cont. • Sketch one of the domains on a number line. • Add a sketch of the other domain. • Write the combined domain in interval notation. Include a “U” in between each set of intervals (if you have more than one).

  17. Domain Restrictions: x ≥ 4, x ≠ 11 Interval Notation:

  18. Domain Restrictions: –10 ≤ x < 14, x ≠ 0 Interval Notation:

  19. Domain Restrictions: x ≥ 0, x < 12 Interval Notation:

  20. Domain Restrictions: x ≥ 0, x ≠ 0 Interval Notation:

  21. Challenge – Domain Restriction: x ≠ 2 Interval Notation:

  22. Domain Restriction: –6 ≠ x Interval Notation:

  23. Domain Restrictions: x ≠ 1, 7 Interval Notation:

  24. Your Turn: • Complete problems 7 – 14on the “Domain and Interval Notation – Guided Notes” handout

  25. Answers 7. 8. 9. 10. 11. 12. 13. 14.

  26. Golf !!!

  27. Answers 1. (–2, 7) 6. (–∞,4) 2. (–3, 1] 7. (–1, 2) U (2, ∞) 3. [–9, –4] 8. [–5, ∞) 4. [–7, –1] 9. (–2, ∞) 5. (–∞, 6) U (6, 10) U (10, ∞)

  28. What happens we type the following expressions into our calculators? Experiment

  29. *Solving for Restricted Domains Algebraically • In order to determine where the domain is defined algebraically, we actually solve for where the domain is undefined!!! • Every value of x that isn’t undefined must be part of the domain.

  30. *Solving for the Domain Algebraically • In my function, do I have a square root? • Then I solve for the domain by: setting the radicand (the expression under the radical symbol) ≥ 0 and then solve for x

  31. Example • Find the domain of f(x).

  32. *Solving for the Domain Algebraically • In my function, do I have a fraction? • Then I solve for the domain by: setting the denominator ≠ 0 and then solve for what x is not equal to.

  33. Example • Solve for the domain of f(x).

  34. *Solving for the Domain Algebraically • In my function, do I have neither? • Then I solve for the domain by: I don’t have to solve anything!!! • The domain is (–∞, ∞)!!!

  35. Example • Find the domain of f(x). f(x) = x2 + 4x – 5

  36. *Solving for the Domain Algebraically • In my function, do I have both? • Then I solve for the domain by: solving for each of the domain restrictions independently

  37. Example • Find the domain of f(x).

  38. Additional Example • Find the domain of f(x).

  39. ***Additional Example • Find the domain of f(x).

  40. Additional Example • Find the domain of f(x).

  41. Your Turn: • Complete problems 1 – 10 on the “Solving for the Domain Algebraically” handout • #8 – Typo!

  42. Answers: 1. 2. 3. 4. 5.

  43. Answers, cont: 6. 7. 8. 9. 10.

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