We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byFidel Hooe
Modified about 1 year ago
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...
Algebra II - Chapter /10.2 Logarithms and Functions.
Functions and Logarithms Section 1.5. More Function Information… One-to-one function: The y-values are different if the x-values are different –Horizontal.
Algebra 2 Notes May 4, Graph the following equation: What equation is that log function an inverse of? ◦ Step 1: Use a table to graph the exponential.
Logarithms Exponential Equations: Logarithmic Equations: Exponent Base Exponent What it equals.
3.3 Logarithmic Functions and Their Graphs. Logarithmic Functions The inverse of y = b x is y = log b x.
MAC 1105 Section 4.3 Logarithmic Functions. The Inverse of a Exponential Function
2.5.1 MATHPOWER TM 12, WESTERN EDITION 2.5 Chapter 2 Exponents and Logarithms.
Introduction to Logarithmic Functions Unit 3: Exponential and Logarithmic Functions.
1.6 Inverse Functions. Review of things we already know One to One Function: That is, while a function specifies that every x has a unique y, a one to.
Holt Algebra Logarithmic Functions Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic functions.
Exponential Functions Brought to you by Tutorial Services The Math Center.
Chapter 3: Functions and Graphs 3.6: Inverse Functions Essential Question: How do we algebraically determine the inverse of a function.
Goals: Understand logarithms as the inverse of exponents Convert between exponential and logarithmic forms Evaluate logarithmic functions.
3.2 Logarithmic Functions & Their Graphs. Inverses of Exponentials Remember from section 1.6 that if a function is one- to-one (meaning it passes the.
Warm Up Use mental math to evaluate – –5 5. A power has a base of –2 and exponent of 4. Write and evaluate the power. (–2) 4 =
1.6 – Inverse Functions and Logarithms. One-To-One Functions A function is one-to-one if no two domain values correspond to the same range value. Algebraically,
Goals— Recognize and evaluate logarithmic functions with base a Graph Logarithmic functions Recognize, evaluate, and graph natural logs Use logarithmic.
Holt McDougal Algebra Logarithmic Functions 7-3 Logarithmic Functions Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.
Logarithmic Functions. Objective To graph logarithmic functions To graph logarithmic functions To evaluate logatrithms To evaluate logatrithms.
Logarithms the inverse of exponential functions. The logarithmic functions help us work easily with very large or very small numbers…. While calculators.
Holt McDougal Algebra Logarithmic Functions Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic.
© 2010 Pearson Education, Inc. All rights reserved.
Copyright © 2009 Pearson Education, Inc. CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3.
Topic: U6L2 Graphing Exponential Functions, Logarithms & Logarithmic Functions
Logarithms Definition Graphing. What’s a Log? the logarithm of a number to a given base is the power or exponent to which the base must be raised in order.
Sec Write the expression using logs: 2 x =7.2.
Algebra II. If x varies directly as z and k represents the constant of proportionality, what is the equation that models this variation?
Exponential Equations Solved by Logarithms (6.8) Finding the value of the exponent when b x = a.
Q Exponential functions f (x) = a x are one-to-one functions. Q (from section 3.7) This means they each have an inverse function. Q We denote the inverse.
4.4 Evaluate Logarithms and Graph Logarithmic Functions Part 2.
Warm-up: Complete the absolute value column on your graphic organizer Domain Range End Behavior Increasing Interval Decreasing Interval Shift Right 5 Shift.
Graphs of Exponential and Logarithmic Functions. Graph of Exponential Function f ( x ) = b x Domain: ( −∞, ∞ ) or x ∊ ℝ Range: ( 0, ∞ ) or y > 0 Intercept:
Logarithmic Functions Recall that for a > 0, the exponential function f(x) = a x is one-to-one. This means that the inverse function exists, and we call.
Section 3.3a!!!. First, remind me… What does the horizontal line test tell us??? More specifically, what does it tell us about the function This function.
Graph of Logarithmic functions. 1 b 1 b 2 2 Graph of y = log b x b >1 If x = , then y = /b b 1 b /b.
L0garithmic Functions Chapter5Section2. Logarithmic Function Recall in Section 4.3 we talked about inverse functions. Since the exponential function.
Unit 3: Exponential and Logarithmic Functions In this activity you will learn how to solve exponential equations using two methods: the common base method.
Math 1304 Calculus I 1.6 Inverse Functions. 1.6 Inverse functions Definition: A function f is said to be one-to- one if f(x) = f(y) implies x = y. It.
CHAPTER 8 - EXPONENTIAL AND LOGARITHMIC FUNCTIONS Click on a lesson. Algebra 2 Lesson 8-1 Click on a feature. Check Skills You’ll Need Additional Examples.
PRECALCULUS Inverse Relations and Functions. If two relations or functions are inverses, one relation contains the point (x, y) and the other relation.
Logarithms – Solving, Inverses, and Graphs To graph a logarithmic function simply enter it into your calculator: Graph y = log 10 x Since your calculator.
Logarithms Logs ARE EXPONENTS!! Logarithms are a way to rewrite exponential equations. They help us solve equations as well.
Algebra II 7.4: Evaluate Logarithms HW: None Chapter 7 Test: , 7.6: Tuesday, 3/3 Fire:
4.8 Solve Exponential and Logarithmic Inequalities Test 2 Unit 4 over on Wednesday 2/16/2011.
ACT Class Opener: rig_1213_f026.htm rig_1213_f026.htm
© 2017 SlidePlayer.com Inc. All rights reserved.