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Inverse functions: Logarithms and Exponentials Fr. Chris’ Chapter 6 Overview.

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Presentation on theme: "Inverse functions: Logarithms and Exponentials Fr. Chris’ Chapter 6 Overview."— Presentation transcript:

1 Inverse functions: Logarithms and Exponentials Fr. Chris’ Chapter 6 Overview

2 How long for how many? To make one photocopy takes 6 seconds To make 10 copies takes 15 seconds 30 copies takes how long? How many copies can be made in 1 minute?

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4 Notice how if you do both functions, you end up where you began In general

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6 Not all have inverses “Horizontal Line Test” Functions must be “one-to-one” to have an inverse function

7 6.1(403)#50

8 Check (using algebra)

9 Check(using graphic calc) Is it symmetric around the diagonal identity line? (Try 5.ZoomSquare)

10 Now try this one... What is the inverse of this?????

11 www.mathorama.com/hatt/exponential.html

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14 In general... “What power of b gives me A?” is written: so if then

15 6.2(414)#36

16 6.2(414)#44

17 What is e??????? See page 410 or Mathematica Can you find e on your calculator?

18 6.2(414)#48 remember how So both x=6 and x=-2 work!

19 6.2(415)#61

20 6.3 (425)#2, #6 and #10

21 6.3(426) #26 (no calc) So... To check with your calc:

22 The graph of log

23 Horizontal Shift

24 6.3(p426) #54 Right shift by 1...


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