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Determining the Key Features of Function Graphs

Determining the Key Features of Function Graphs. The Key Features of Function Graphs - Preview. Domain and Range x-intercepts and y-intercepts Intervals of increasing, decreasing, and constant behavior Parent Equations Maxima and Minima. Domain.

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Determining the Key Features of Function Graphs

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  1. Determining the Key Features of Function Graphs

  2. The Key Features of Function Graphs - Preview • Domain and Range • x-intercepts and y-intercepts • Intervals of increasing, decreasing, and constant behavior • Parent Equations • Maxima and Minima

  3. Domain • To find the domain of the graph _____________________of the graph

  4. → → Determining Domain - Symbols

  5. Determining Domain • Start at the origin • Return to the origin

  6. Examples Domain: Domain:

  7. Example Domain:

  8. Determining Domain - Infinity Domain:

  9. Examples Domain: Domain:

  10. Your Turn: • In the purple Precalculus textbooks, complete problems 3, 7, and find the domain of 9 and 10 on pg. 160 3. 7. 9. 10.

  11. Range • To find the range of the graph _____ _________________of the graph • We also use open and closed circles for the range

  12. Determining Range • Start at the origin • Return to the origin

  13. Examples Range: Range:

  14. Examples Range: Range:

  15. Your Turn: • In the purple Precalculus textbooks, complete problems 4, 8, and find the range of 9 and 10 on pg. 160 4. 8. 9. 10.

  16. X-Intercepts • Has many names: • x-intercept • Roots • Zeros

  17. Examples x-intercepts: x-intercepts:

  18. Y-Intercepts y-intercepts: y-intercepts:

  19. Seek and Solve!!!

  20. Types of Function Behavior • 3 types: • Increasing • Decreasing • Constant • When determining the type of behavior, ____________________________________________________________________

  21. Roller Coasters!!! Fujiyama in Japan

  22. Types of Behavior – Increasing • Direct Relationship

  23. Types of Behavior – Constant

  24. Types of Behavior – Decreasing • Inverse Relationship

  25. Identifying Intervals of Behavior Increasing: [0, 4) The y-values are increasing the x-values are between 0 inclusive and 4 exclusive when

  26. Identifying Intervals of Behavior y • Increasing: • Constant: • Decreasing: x 1 1

  27. Identifying Intervals of Behavior, cont. y • Increasing: • Constant: • Decreasing: x -3 -1 Don’t get distracted by the arrows! Even though both of the arrows point “up”, the graph isn’t increasing at both ends of the graph!

  28. Your Turn: • Complete problems 1 – 4 on The Key Features of Function Graphs – Part II handout.

  29. 1. 2. 3. 4.

  30. What do you think of when you hear the word parent?

  31. Parent Function Flipbook

  32. Parent Function • The most basic form of a type of function • Determines the general shape of the graph

  33. Linear Absolute Value Greatest Integer Quadratic Cubic Square Root Cube Root Reciprocal Basic Types of Parent Functions

  34. Identifying Parent Equations • From Graphs:

  35. Examples

  36. Your Turn: • Complete problems 5 – 12 on The Key Features of Function Graphs handout

  37. Maximum (Maxima) and Minimum (Minima) Points

  38. Identifying Minimum and Maximum Points • You can have any combination of min and max points • Minimum: • Maximum:

  39. Examples

  40. Your Turn: • Complete problems 1 – 6 on The Key Features of Function Graphs – Part III handout.

  41. Find f(#) Find the value of f(x) when x equals #. Solve for f(x) or y! Find f(x) = # Find the value of x when f(x) equals #. Solve for x! Reminder: Find f(#) and Find f(x) = x

  42. Evaluating Graphs of Functions – Find f(#) • f(1) = • f(–2) =

  43. Evaluating Graphs of Functions – Find f(x) = # • f(x) = –2 • f(x) = 2

  44. Example • Find f(1) • Find f(–0.5) • Find f(x) = 0 • Find f(x) = –5

  45. Your Turn: • Complete Parts A – D for problems 7 – 14 on The Key Features of Function Graphs – Part III handout.

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