1. Graphing Exponential Functions
LESSON 7–1
Graphing Exponential Functions

2. TEKS

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

4. exponential function exponential growth asymptote growth factor
exponential decay
decay factor
Vocabulary

5. Concept

6. 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

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

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

9. Concept

10. 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

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

12. 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

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

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

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

16. 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

17. Graph Exponential Growth Functions
Answer:
Example 3

18. 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

19. Concept

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

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

22. 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

23. ● 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

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

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

26. 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 50 miles.
y = a(1 – r)t
= 14.7(1 – 0.20)t
= 14.7(0.80)t
Example 5A

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

28. 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

29. 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

30. 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

31. Logarithms and Logarithmic Functions
LESSON 7–3
Logarithms and Logarithmic Functions

32. Targeted TEKS
A2.2(C) Describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), includingthe restriction(s) on domain, which will restrict its range.
A2.5(C) Rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations.
Also addresses A2.2(A) and A2.5(A).
Mathematical Processes
A2.1(B), Also addresses A2.1(G).
TEKS

33. You found the inverse of a function.
Evaluate logarithmic expressions.
Graph logarithmic functions.
Then/Now

34. logarithm
logarithmic function
Vocabulary

35. Concept

36. Concept

37. A. Graph the function f(x) = log3 x.
Graph Logarithmic Functions
A. Graph the function f(x) = log3 x.
Step 1 Identify the base.
b = 3
Step 2 Determine points on the graph.
Because 3 > 1, use the points (1, 0), and (b, 1).
Step 3 Plot the points and sketch the graph.
Example 4

38. Graph Logarithmic Functions
(1, 0)
(b, 1) → (3, 1)
Answer:
Example 4

39. Step 2 Determine points on the graph.
Graph Logarithmic Functions
B. Graph the function
Step 1 Identify the base.
Step 2 Determine points on the graph.
Example 4

40. Graph Logarithmic Functions
Step 3 Sketch the graph.
Answer:
Example 4

41. A. Graph the function f(x) = log5x.
A. B.
C. D.
Example 4

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

43. Concept

44. This represents a transformation of the graph f(x) = log6 x.
Graph Logarithmic Functions
This represents a transformation of the graph f(x) = log6 x.
● : The graph is compressed vertically.
● h = 0: There is no horizontal shift.
● k = –1: The graph is translated 1 unit down.
Example 5

45. Graph Logarithmic Functions
Answer:
Example 5

46. ● |a| = 4: The graph is stretched vertically.
Graph Logarithmic Functions
● |a| = 4: The graph is stretched vertically.
● h = –2: The graph is translated 2 units to the left.
● k = 0: There is no vertical shift.
Example 5

47. Graph Logarithmic Functions
Answer:
Example 5

48. A. B.
C. D.
Example 5

49. A. B.
C. D.
Example 5

50. Graphing Exponential Functions
LESSON 7–1
Graphing Exponential Functions