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Warm Up

Warm Up. Evaluate f ( x ) = 4 x – 7 over the domain {1, 2, 3, 4}. What is the range?. How do we interpret and represent functions? F.IF.6 Functions Lesson 3: Identifying key features of a graph. Identifying Key Features of a Graph. Intercepts: X-intercept: .

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Warm Up

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  1. Warm Up Evaluate f(x) = 4x – 7 over the domain {1, 2, 3, 4}. What is the range?

  2. How do we interpret and represent functions? F.IF.6Functions Lesson 3:Identifying key features of a graph

  3. Identifying Key Features of a Graph Intercepts: X-intercept: The place on the x-axis where the graph crosses the axis

  4. Example 1 Identify the x-intercepts:

  5. Example 2 Identify the x-intercepts:

  6. Example 3 Identify the x-intercepts:

  7. Identifying Key Features of a Graph Intercepts: y-intercept: The place on the y-axis where the graph crosses the axis

  8. Example 1 Identify the y-intercepts:

  9. Example 2 Identify the y-intercepts:

  10. Example 3 Identify the y-intercepts:

  11. Identifying Key Features of a Graph 1. Intercepts: Find the x and y intercepts of the following graph. ?

  12. Identifying Key Features of a Graph Increasing or Decreasing???? Increasing: A function is said to increase if while the values for x increase as well as the values for y increase. (Both x and y increase)

  13. Identifying Key Features of a Graph Increasing or Decreasing???? Decreasing: A function is said to decrease if one of the variables increases while the other variable decreases. (Ex: x increases, but y decreases)

  14. Example 1 Increasing or decreasing?

  15. Example 2 Increasing or decreasing?

  16. Identifying Key Features of a Graph Intervals: An interval is a continuous series of values. (Continuous means “having no breaks.)

  17. Identifying Key Features of a Graph Intervals: • A function is positive when its graph is above the x-axis. • The function is negative when its graph is below the x-axis.

  18. Identifying Key Features of a Graph The function is positive when x > ? When x > 4!

  19. Example 1 Part 1 The function is positive when x _ __?

  20. Example 1 Part 2 The function is negative when x _ __ ?

  21. Example 2 Part 1 The function is positive when x _ __ ?

  22. Example 2 Part 2 The function is negative when x _ __ ?

  23. Identifying Key Features of a Graph Extrema: • A relative minimum is the point that is the lowest, or the y-value that is the least for a particular interval of a function. • A relative maximum is the point that is the highest, or the y-value that is the greatest for a particular interval of a function. • Linear and exponential functions will only have a relative minimum or maximum if the domain is restricted

  24. Identifying Key Features of a Graph Domain and Range: Domain: all possible input values Range: all possible output values

  25. Remember your numbers when describing domain and range… Natural numbers: 1, 2, 3, ... Whole numbers: 0, 1, 2, 3, ... Integers: ..., –3, –2, –1, 0, 1, 2, 3, ... Rational numbers: numbers that can be written as a fraction, terminating decimal or repeating decimal Irrational numbers: numbers that cannot be written as a fraction, terminating decimal or repeating decimal Real numbers: the set of all rational and irrational numbers

  26. Example 1 What is the domain? Range?

  27. Example 2 What is the domain? Range?

  28. Identifying Key Features of a Graph Asymptotes: A line that the graph gets closer and closer to, but never crosses or touches.

  29. Example 1 Identify the asymptote:

  30. Example 2 Identify the asymptote:

  31. Identifying Key Features of a Graph Identify the following: Type of function Domain and Range Increasing or Decreasing Extrema Guided Practice Example 1 • A taxi company in Atlanta charges $2.75 per ride plus $1.50 for every mile driven. Determine the key features of this function.

  32. Identifying Key Features of a Graph Guided Practice Example 2: • Identify the following: • Type of function • Domain and range • Increasing or decreasing • Asymptote

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