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

Legend of the Chessboard https://www.youtube.com/watch?v=t3d0Y-JpRRg Or 9 quintillion Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

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? Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Try it on your parents If they agree how much will they owe your on the 31st day? Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Try it on your parents If you continued the process how long would it take to make a billion dollars? Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

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. Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

What function represents this situation? Pyramid Schemes What function represents this situation? Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

Exponential vs. Power Functions Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

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 ¼ (-2, ¼) -1 ½ (-1, ½) 1 (0, 1) 2 (1, 2) 4 (2, 4) 4 2 x –2 2 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Graph f(x) = 2x

In your packet: Complete part I on the 2nd page (Exponential/Logarithmic Graphing). Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Graph f(x) = 2x

What do you notice? Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Graph f(x) = 2x

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: (–, ) Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Graph of Exponential Function (a > 1)

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: (–, ) Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Graph of Exponential Function (0 < a < 1)

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

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

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, ) Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Translation of Graph

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, ) Copyright © by Houghton Mifflin Company, Inc. All rights reserved. Example: Reflection of Graph

Draw a rough sketch of what you think each function will look like – then verify on a graphing calculator Desmos.com Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

What is e? Complete #a-e on page 3 https://www.youtube.com/watch?v=yTfHn9Aj7UM (1st 6 mins) Complete #a-e on page 3 Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

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 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. The number e

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 Copyright © by Houghton Mifflin Company, Inc. All rights reserved.