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Factoring Practice (5 questions)

Factoring Practice (5 questions). Factoring Practice (Answers). Exponential Functions and Their Graphs Sections 7-1,2,3. Objectives. I can recognize growth or decay exponential equations I can graph exponential growth and decay parent functions. Definition of Exponential Function.

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Factoring Practice (5 questions)

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  1. Factoring Practice (5 questions)

  2. Factoring Practice (Answers)

  3. Exponential Functions and Their GraphsSections 7-1,2,3

  4. Objectives • I can recognize growth or decay exponential equations • I can graph exponential growth and decay parent functions

  5. Definition of Exponential Function The exponential function f with base b is defined by f(x) = bx where b > 0, b 1, and x is any real number. For instance, f(x) = 3x and g(x) = 0.5x are exponential parent functions.

  6. The graph off(x) = bx, b > 1 Graph of Exponential Function (a > 1) Exponential Growth y 4 Range: (0, ) (0, 1) x 4 Horizontal Asymptote y = 0 Domain: (–, )

  7. The graph off(x) = bx, 0 < b < 1 Graph of Exponential Function (0 < a < 1) y Exponential Decay 4 Range: (0, ) Horizontal Asymptote y = 0 (0, 1) x 4 Domain: (–, )

  8. Example: Sketch the graph ofy = 2x. Example: Graph f(x) = 2x y 4 2 x –2 2

  9. Base is 2. Base is 10. Base is 3. Definition of the Exponential Function Put these in your calculator as y1=, y2=, y3= And graph them simultaneously Here are some examples of exponential functions. f (x) = 2xg(x) = 10xh(x) = 3x

  10. When base is a fraction • Graph the following on your calculator at the same time • y1 = (1/2)x • y2= (3/4)x • y3 = (7/8)x

  11. Example: Sketch the graph ofg(x) = 2-x. State the domain and range. Example: Reflection of Graph y f(x) = 2x The graph of this function is a reflection the graph of f(x) = 2x in the y-axis. 4 Domain: (–, ) x –2 2 Range: (0, )

  12. The graph off(x) = ex Graph of Natural Exponential Function f(x) = ex y 6 4 2 x –2 2

  13. The number e The irrational number e, where e 2.718281828… is used in applications involving growth and decay. It is a key on your calculator in the first comlum 2nd LN

  14. What type is it?? • You must know if you are graphing a growth or decay equation? • Let’s look at some examples

  15. Reflection Transformations

  16. Reflections Change Type of Exponential

  17. Growth or Decay??

  18. Growth or Decay??

  19. Growth or Decay??

  20. Growth or Decay??

  21. Growth or Decay??

  22. Growth or Decay??

  23. Growth or Decay??

  24. Homework • Worksheet 11-1

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