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Dive into exponential growth and decay functions, learn transformations, graphing examples, and real-world applications. Enhance your math skills with interactive exercises and new vocabulary.

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  1. Splash Screen

  2. Five-Minute Check (over Chapter 6) CCSS Then/Now New Vocabulary Key Concept: Parent Function of Exponential Growth Functions Example 1: Graph Exponential Growth Functions Key Concept: Transformations of Exponential Functions Example 2: Graph Transformations Example 3: Real-World Example: Graph Exponential Growth Functions Key Concept: Parent Function of Exponential Decay Functions Example 4: Graph Exponential Decay Functions Example 5: Real-World Example: Graph Exponential Decay Functions Lesson Menu

  3. A.± 1 B.± C.± 2 D.2, 3 2 __ __ 2 3 Solve 4a2 – 9 = 0. 5-Minute Check 1

  4. A.± 1 B.± C.± 2 D.2, 3 2 __ __ 2 3 Solve 4a2 – 9 = 0. 5-Minute Check 1

  5. A.3, 2, 1 B. C. D. Solve 6y3 + 13y2 + 5y = 0. 5-Minute Check 2

  6. A.3, 2, 1 B. C. D. Solve 6y3 + 13y2 + 5y = 0. 5-Minute Check 2

  7. Find (f + g)(x) if f(x) = 3x + 7 and g(x) = x2 – 10. A.(f + g)(x) =3x2 – 70 B.(f + g)(x) =x2 + 3x – 3 C.(f + g)(x) =x2 – 3x + 17 D.(f + g)(x) =3x – 3 5-Minute Check 3

  8. Find (f + g)(x) if f(x) = 3x + 7 and g(x) = x2 – 10. A.(f + g)(x) =3x2 – 70 B.(f + g)(x) =x2 + 3x – 3 C.(f + g)(x) =x2 – 3x + 17 D.(f + g)(x) =3x – 3 5-Minute Check 3

  9. Determine whether f(x) = 4x – 9 and g(x) = are inverse functions. A. yes B. no 5-Minute Check 4

  10. Determine whether f(x) = 4x – 9 and g(x) = are inverse functions. A. yes B. no 5-Minute Check 4

  11. A. –9xy2 B. –9x2y4 C. –3xy2 D. 3xy2 5-Minute Check 5

  12. A. –9xy2 B. –9x2y4 C. –3xy2 D. 3xy2 5-Minute Check 5

  13. A.–7 B. C.–2 D.4 5-Minute Check 6

  14. A.–7 B. C.–2 D.4 5-Minute Check 6

  15. Content Standards F.IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F.IF.8.b Use the properties of exponents to interpret expressions for exponential functions. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. CCSS

  16. You graphed polynomial functions. • Graph exponential growth functions. • Graph exponential decay functions. Then/Now

  17. exponential function • exponential growth • asymptote • growth factor • exponential decay • decay factor Vocabulary

  18. Concept

  19. Graph Exponential Growth Functions Graph y = 4x. State the domain and range. Make a table of values. Connect the points to sketch a smooth curve. Example 1

  20. Graph Exponential Growth Functions Answer: Example 1

  21. Graph Exponential Growth Functions Answer: The domain is all real numbers, and the range is all positive real numbers. Example 1

  22. A.B. C.D. Which is the graph of y = 3x? Example 1

  23. A.B. C.D. Which is the graph of y = 3x? Example 1

  24. Concept

  25. Graph Transformations A. Graph the function y = 3x – 2. State the domain and range. The equation represents a translation of the graphy = 3x down 2 units. Example 2A

  26. Graph Transformations Answer: Example 2A

  27. Graph Transformations Answer: Domain = {all real numbers} Range = {y│y > –2} Example 2A

  28. Graph Transformations B. Graph the function y = 2x – 1. State the domain and range. The equation represents a translation of the graphy = 2x right 1 unit. Example 2B

  29. Graph Transformations Answer: Example 2B

  30. Graph Transformations Answer: Domain = {all real numbers} Range = {y │y ≥ 0} Example 2B

  31. A.B. C.D. A. Graph the function y = 2x – 4. Example 2A

  32. A.B. C.D. A. Graph the function y = 2x – 4. Example 2A

  33. A.B. C.D. B. Graph the function y = 4x – 2+ 3. Example 2B

  34. A.B. C.D. B. Graph the function y = 4x – 2+ 3. Example 2B

  35. Graph Exponential Growth Functions INTERNETIn 2006, there were 1,020,000,000 people worldwide using the Internet. At that time, the number of users was growing by 19.5% annually. Draw a graph showing how the number of users would grow from 2006 to 2016 if that rate continued. First, write an equation using a = 1.020 (in billions), and r = 0.195. y = 1.020(1.195)t Then graph the equation. Example 3

  36. Graph Exponential Growth Functions Answer: Example 3

  37. Graph Exponential Growth Functions Answer: Example 3

  38. A.B. C.D. CELLULAR PHONESIn 2006, there were about 2,000,000,000 people worldwide using cellular phones. At that time, the number of users was growing by 11% annually. Which graph shows how the number of users would grow from 2006 to 2014 if that rate continued? Example 3

  39. A.B. C.D. CELLULAR PHONESIn 2006, there were about 2,000,000,000 people worldwide using cellular phones. At that time, the number of users was growing by 11% annually. Which graph shows how the number of users would grow from 2006 to 2014 if that rate continued? Example 3

  40. Concept

  41. A. Graph the function State the domain and range. Graph Exponential Decay Functions Example 4A

  42. Graph Exponential Decay Functions Answer: Example 4A

  43. Graph Exponential Decay Functions Answer: Domain = {all real numbers} Range = {y│y > 0} Example 4A

  44. B. Graph the function State the domain and range. The equation represents a transformation of the graph of Graph Exponential Decay Functions Examine each parameter. ● There is a negative sign in front of the function: The graph is reflected in the x-axis. ● a = 4: The graph is stretched vertically. Example 4B

  45. Graph Exponential Decay Functions ● h = 1: The graph is translated 1 unit right. ● k = 2: The graph is translated 2 units up. Answer: Example 4B

  46. Graph Exponential Decay Functions ● h = 1: The graph is translated 1 unit right. ● k = 2: The graph is translated 2 units up. Answer: Domain = {all real numbers} Range = {y│y < 2} Example 4B

  47. A. Graph the function A.B. C.D. Example 4A

  48. A. Graph the function A.B. C.D. Example 4A

  49. B. Graph the function A.B. C.D. Example 4B

  50. B. Graph the function A.B. C.D. Example 4B

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