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Inverse functions: Logarithms and Exponentials Fr. Chris’ Chapter 6 Overview
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?
Notice how if you do both functions, you end up where you began In general
Not all have inverses “Horizontal Line Test” Functions must be “one-to-one” to have an inverse function
Check (using algebra)
Check(using graphic calc) Is it symmetric around the diagonal identity line? (Try 5.ZoomSquare)
Now try this one... What is the inverse of this?????
In general... “What power of b gives me A?” is written: so if then
What is e??????? See page 410 or Mathematica Can you find e on your calculator?
6.2(414)#48 remember how So both x=6 and x=-2 work!
6.3 (425)#2, #6 and #10
6.3(426) #26 (no calc) So... To check with your calc:
The graph of log
6.3(p426) #54 Right shift by 1...
Quadratic Equations, Solving a Quadratic Equation by factorization by graphical method by taking square roots by quadratic equation.
Of. and a to the in is you that it at be.
Chapter 2 Section 4 Solving Equations with variables on both sides- YES!
The. of and a to in is you that it he was.
High Frequency Words List A Group 1. the of and.
Logarithmic Functions Logarithmic Functions and Models.
Sec Write the expression using logs: 2 x =7.2.
Discuss the equality property of exponential equation.
The. of and a to in is you that it he for.
Weve looked at linear and quadratic functions, polynomial functions and rational functions. We are now going to study a new function called exponential.
8.3 – Logarithmic Functions and Inverses. What is a logarithm? A logarithm is the power to which a number must be raised in order to get some other number.
1 6.4 Logarithmic Functions In this section, we will study the following topics: Evaluating logarithmic functions with base a Graphing logarithmic functions.
Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions.
Can you see?. I like him. When will we go? All or some.
3: Graphs of Inverse Functions © Christine Crisp Teach A Level Maths Vol. 2: A2 Core Modules.
Copyright © Cengage Learning. All rights reserved. 1.6 Inverse Functions.
Lap 1. the to and he a I you it of in Lap 2.
What time is it? Time to solve equations!. Chapter 2: Section 1 Solving One-Step Equations.
First let’s review 5.1 Write the equation in slope-intercept form, given m = 3 ang b = (0,-2) Example m = 3, b = (0,-2) y = __ x + ___ y = mx + b.
3.4 Inverse Functions & Relations. Inverse Relations Two relations are inverses if and only if one relation contains the element (b, a) whenever the other.
Lesson 3.4 – Zeros of Polynomial Functions Rational Zero Theorem Represent a polynomial equation of degree n. If a rational number, where p and q have.
Graphical Transformations Vertical and Horizontal Translations Vertical and Horizontal Stretches and Shrinks.
Lets build fluency! The people By the water You and I.
Please answer the following multiple choice questions. Click on your answer. Please feel free to use paper or graphing calculators to find the correct.
High-Frequency Phrases First 100 Words. The people.
Section 1.6 – Inverse Functions Section Logarithms.
Logarithmic Equations Solving Logarithmic Equations.
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