1. Unit 8-1: Graphing Exponential Functions

2. Then/Now Graph exponential growth functions.
Graph exponential decay functions.

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

4. Concept (Pg. 451)

5. Example 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.

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

7. Concept (pg. 452)

8. Example 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.

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

10. Example 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.

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

12. Example
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.

13. Example
Graph Exponential Growth Functions
Answer:

14. Concept (pg. 453)

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

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

17. Example 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.

18. Example ● 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}

19. Example
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

20. Example
Graph Exponential Decay Functions
Graph the equation.
Answer:

21. Example
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.

22. Assignment Pg. 455 #2-4 all (Graph) #7 #12 #34