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Understanding Graph Characteristics: Domain, Range, and Intervals of Increase and Decrease

This guide explores the characteristics of a graph, including domain, range, maximum and minimum points, and intervals of increase and decrease. For discrete graphs, simply list the domain and range without duplicates. Continuous graphs use interval notation to express their domain and range. Special cases are highlighted, such as when dealing with open and closed circles. The guide also defines zeros as x-intercepts, identifies y-intercepts, and explains how to trace a graph to determine increasing, decreasing, and constant intervals.

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Understanding Graph Characteristics: Domain, Range, and Intervals of Increase and Decrease

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  1. 6 Parent Graphs

  2. Characteristics of a graph(Lots of Vocabulary)Domain, Range, Max, Min, Zero, Y-Intercept, Interval of Increase, and Interval of Decrease

  3. Finding Domain & Range Given: • Discrete graphs – you just LIST the domain and range (don’t repeat and list in order from least to greatest) • Continuous graphs – use interval notation (least, greatest)

  4. Find the Domain and Range

  5. Find the Domain and Range

  6. Set Notation Uses: Is used when there is a open dot or the number is NOT included on the graph. Is used when there is a closed dot or when the number is included on the graph. Is used when one number is excluded.

  7. Domain and Range: Graph

  8. Domain and Range: Graph

  9. Domain and Range: Graph Special case: When there is an open circle and closed circle on the same number – go with the closed circle.

  10. Domain and Range: Graph

  11. Domain and Range: Graph

  12. Domain and Range: Graph

  13. Maximum or Minimum Point • Max. Point – is the HIGHEST on the graph • Min. Point – is the LOWEST on the graph (x, y)

  14. Maximum or Minimum Value?Where? Max. Point (0, 4)

  15. Maximum or Minimum Value?Where? Min. Point (-1, -9)

  16. ZEROSare the same thing as theX-INTERCEPTS. (x, y)

  17. Name the zeros. (-4, 0) and (3, 0)

  18. Name the Y-INTERCEPT. (0, -4)

  19. Interval of Increase, Interval of Decrease, & Constant Graphs To find where the graph is increasing and decreasing, trace the graph with your finger from left to right. Specify the x-values!

  20. Increasing, Decreasing, & Constant: Graphs • If your finger is going up, the graph is increasing. • If your finger is going down, the graph is decreasing. • If your finger goes neither up or down…then the graph is CONSTANT.

  21. Find the interval of decrease. The x-values where the graph is going down. Decreasing

  22. Find the interval of increase The x-values where the graph is going up. Increasing

  23. Interval of increase: Interval of decrease:

  24. Interval of increase: Interval of decrease:

  25. Home Work First part of Fences Task

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