1. 3-1
Exponential Functions and Their Graphs – you’ll need a graphing calculator for today’s stuff.

2. Legend of the Chessboard
Or 9 quintillion
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3. Try it on your parents
For your chores for the month ask to be paid a penny on the first day, 2 pennies the second, 4 the third so on and so forth for all 31 days of the month.
If they agree how much will they owe your on the 31st day?
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4. Try it on your parents
If they agree how much will they owe your on the 31st day?
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5. Try it on your parents
If you continued the process how long would it take to make a billion dollars?
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6. The 6 recruits each pay the recruiter $100.
Pyramid Schemes
One person recruits 6 other people to participate in a "no-fail investment opportunity."
The 6 recruits each pay the recruiter $100.
The recruiter now tells them to go out and recruit 6 more people to do the same.
If each recruit is successful, they'll all end up with $500 in profit from a $100 investment.
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7. What function represents this situation?
Pyramid Schemes
What function represents this situation?
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8. Exponential vs. Power Functions
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9. On page 1 of your packet: Sketch the graph of f(x) = 2x.
Complete the top row for Exponential Functions y x
f(x)
(x, f(x)) -2
(-2, ¼) -1
(-1, ½) 1
(0, 1) 2
(1, 2) 4
(2, 4) 4 2 x –2 2
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Example: Graph f(x) = 2x

10. In your packet: Complete part I on the 2nd page (Exponential/Logarithmic Graphing).
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Example: Graph f(x) = 2x

11. What do you notice?
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Example: Graph f(x) = 2x

12. Graph of Exponential Function (a > 1)
The graph of f(x) = ax, a > 1 y 4
Range: (0, )
(0, 1) x 4
Horizontal Asymptote y = 0
Domain: (–, )
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Graph of Exponential Function (a > 1)

13. Graph of Exponential Function (0 < a < 1)
The graph of f(x) = ax, 0 < a < 1 y 4
Range: (0, )
Horizontal Asymptote y = 0
(0, 1) x 4
Domain: (–, )
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Graph of Exponential Function (0 < a < 1)

14. Review of Transformations
Or reflection
over y-axis!
Or reflection
over x-axis!

15. Review of Transformations
Do non-rigid transformation 1st (strech/compress)
Then rigid transformations (up/down and left/right)
Review of Transformations

16. Example: Translation of Graph
Example: Sketch the graph of g(x) = 2x – 1. State the domain and range. y
f(x) = 2x
The graph of this function is a vertical translation of the graph of f(x) = 2x down one unit . 4 2
Domain: (–, ) x
y = –1
Range: (–1, )
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Example: Translation of Graph

17. Example: Reflection of Graph
Example: Sketch the graph of g(x) = 2-x. State the domain and range. 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, )
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Example: Reflection of Graph

18. Draw a rough sketch of what you think each function will look like – then verify on a graphing calculator
Desmos.com
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19. What is e? Complete #a-e on page 3
(1st 6 mins)
Complete #a-e on page 3
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20. The irrational number e, where e  2.718281828…
we can use 2.72 for an approximation of e
is used in applications involving growth and decay.
Using techniques of calculus, it can be shown that
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The number e

21. H Dub: Pg 1 and 2 – top half Pg 3 – #1-3 and a-e Pg 4 – #1-10
Desmos.com
H Dub:
Pg 1 and 2 – top half
Pg 3 – #1-3 and a-e
Pg 4 – #1-10
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