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Understanding Linear vs Nonlinear Functions and Exponential Behavior

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This review covers the differentiation between linear and nonlinear functions through practical examples. Students will learn how to graph exponential functions and identify datasets that exhibit exponential behavior. Key concepts include graphing functions like y = 3x + 1, determining y-intercepts, and stating domain and range. The lesson also explores the implications of exponential growth using real-world examples, such as bacteria doubling over time. Students will solidify their understanding through quizzes and homework assignments.

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Understanding Linear vs Nonlinear Functions and Exponential Behavior

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  1. Bell Ringer # 5 (Quick Review) • Linear or Nonlinear? y = 3x + 1 • Linear or nonlinear? 3x = 4 • Linear or nonlinear? y = x2

  2. Chapter 7.5 NotesObjectives • SWBAT graph exponential functions. • SWBAT identify data that display exponential behavior. CCRS: 30c, and 38

  3. Exponential Function

  4. Example: Graph with a>0and b>1. Graph y = 3x. Find the y-intercept, and state the domain and range.

  5. Example #1 • Graph y = 7x Find the y-intercept and state the domain and range.

  6. Example: Graph a>0 and 0<b<1 • Graph y = (1/3)x. Find the y-intercept, and state the domain and range.

  7. Example #2 • Graph y = ( ½ )x – 1. Find the y-intercept, and state the domain and range.

  8. Graphs of Exponentials

  9. Graphs of Exponentials

  10. Example:UseExponentials a) Graph the function. What values of C and t are meaningful in the context of the problem? b) How much soda was consumed in 2005?

  11. Example #3: A certain bacteria population doubles every 20 minutes. Beginning with 10 cells in a culture, the population can be represented by the function B = 10 (2)t, where B is the number of bacteria cells and t is the time in 20 minute increments. How many will there be after 2 hours?

  12. Example: Identify Exponential Behavior • Determine whether the set of data shown below displays exponential behavior. Write yes or no. Explain.

  13. Example #4 Determine whether the set of data shown below displays exponential behavior. Write yes or no. Explain why or why not.

  14. Quick Quiz Graph each function. Find the y-intercept and state the domain and range. • y = 2x • f(x) = 6x + 3 HOMEWORK: TB pg. 427 (10-24 evens; 46-49)

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