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

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

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

6. Solve 6y3 + 13y2 + 5y = 0.
A. 3, 2, 1 B. C. D.
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. Mathematical Practices
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 y = 4x. State the domain and range.
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. Which is the graph of y = 3x?
A. B.
C. D.
Example 1

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

24. Concept

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

26. Graph Transformations
Answer:
Example 2A

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

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

29. Graph Transformations
Answer:
Example 2B

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

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

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

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

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

35. First, write an equation using a = 1.020 (in billions), and r = 0.195.
Graph Exponential Growth Functions
INTERNET In 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 = (in billions), and r =
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. CELLULAR PHONES In 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?
A. B.
C. D.
Example 3

39. CELLULAR PHONES In 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?
A. B.
C. D.
Example 3

40. Concept

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

42. Graph Exponential Decay Functions
Answer:
Example 4A

43. Domain = {all real numbers} Range = {y│y > 0}
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.
Graph Exponential Decay Functions
B. Graph the function State the domain and range.
The equation represents a transformation of the graph of
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. ● h = 1: The graph is translated 1 unit right.
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. ● h = 1: The graph is translated 1 unit right.
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

51. Graph Exponential Decay Functions
A. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in2 at Earth’s surface. It decreases by about 20% for each mile of altitude up to about 50 miles. Draw a graph to represent atmospheric pressure for altitude from 0 to 20 miles.
y = a(1 – r)t
= 14.7(1 – 0.20)t
= 14.7(0.80)t
Example 5A

52. Graph the equation. Answer: Graph Exponential Decay Functions
Example 5A

53. Graph the equation. Answer: Graph Exponential Decay Functions
Example 5A

54. y = 14.7(0.80)t Equation from part a.
Graph Exponential Decay Functions
B. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in2 at Earth’s surface. It decreases by about 20% for each mile of altitude up to about 50 miles. Estimate the atmospheric pressure at an altitude of 10 miles.
y = 14.7(0.80)t Equation from part a.
= 14.7(0.80)10 Replace t with 10.
≈ 1.58 lb/in2 Use a calculator.
Answer:
Example 5B

55. y = 14.7(0.80)t Equation from part a.
Graph Exponential Decay Functions
B. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in2 at Earth’s surface. It decreases by about 20% for each mile of altitude up to about 50 miles. Estimate the atmospheric pressure at an altitude of 10 miles.
y = 14.7(0.80)t Equation from part a.
= 14.7(0.80)10 Replace t with 10.
≈ 1.58 lb/in2 Use a calculator.
Answer: The atmospheric pressure at an altitude of about 10 miles will be approximately lb/in2.
Example 5B

56. A. AIR PRESSURE The pressure of a car tire with a bent rim is 34
A. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Draw a graph to represent the air pressure for a trip from 0 to 40 miles.
A B.
C D.
Example 5A

57. A. AIR PRESSURE The pressure of a car tire with a bent rim is 34
A. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Draw a graph to represent the air pressure for a trip from 0 to 40 miles.
A B.
C D.
Example 5A

58. B. AIR PRESSURE The pressure of a car tire with a bent rim is 34
B. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Estimate the air pressure of the tire after 20 miles.
A lb/in2
B lb/in2
C lb/in2
D lb/in2
Example 5B

59. B. AIR PRESSURE The pressure of a car tire with a bent rim is 34
B. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Estimate the air pressure of the tire after 20 miles.
A lb/in2
B lb/in2
C lb/in2
D lb/in2
Example 5B

60. End of the Lesson