Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 4b – More on Logarithms Mini-Lesson Problem 8 WORKED EXAMPLE – GRAPHING LOGARITHMIC FUNCTIONS The Logarithmic Function in Problem 7 is of the form ( ) ( ). All Logarithmic Functions of this form share key characteristics. In this example, we look at a typical graph of this type of function and list the key characteristics in the table below. ( ) ( ) Domain x > 0 (all positive real numbers) Range All real numbers x-intercept (1, 0) y-intercept Does not cross the y-axis so no y-intercept Y-axis is a guiding line for the graph Left to Right Behavior Y-values (outputs) increasing but more and more slowly (at a decreasing rate) Values of x for which f(x) >0 x > 1 Values of x for which f(x)
Lesson 4b – More on Logarithms Mini-Lesson Modeling Data with Logarithmic Regression Just as we did with Linear and Exponential Functions, we can model appropriate data using regression. The steps are very similar to the other processes we have used. We will use a slightly different type of logarithm for this regression denoted by LN or Natural Logarithm. You will learn more about this in later classes. Problem 10 WORKED EXAMPLE – LOGARITHMIC REGRESSION Determine if the data set below can be modeled by a logarithmic function. If so, find that function rounding all decimals to 4 places. x .5 1 2 3 4 5 y -10 .8 4.3 6.2 7.1 8 Step 1: Insert data into L1, L2 list using Stat>Edit. Your data should look the same as in the table on the right. Step 2: Turn on your Plot (Go to Y= and highlight Plot 1) then select Zoom9 to work with a good window for your data. Your graph should look the same as the table on the right. The data are increasing but at a decreasing rate and generally have the shape of a logarithmic graph. We should be able to model the data effectively with a logarithmic equation. Step 3: Go to Stat>Calc>9:LnReg to find the Logarithmic Regression model for the data. Step 4: Press Enter twice to form the equation information on your screen. Write the equation as y = -2.2274 + 7.2698 Ln x Step 5: Enter the equation into your Y= list and press Graph to show the graph of the data and the model. Looks like the model is a pretty good approximation of our data set. Scottsdale Community College Page 171 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 1b - Linear Equations In the
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Lesson 1b - Linear Equations Mini-L
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Lesson 2b - Functions and Function
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Lesson 5b - Solving Quadratic Equat
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Lesson 6a - Exponents and Rational
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Lesson 6b - Rational Exponents & Ra
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Lesson 6b - Rational Exponents and
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Appendix A: You Try Answers Lesson
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Appendix A: You Try Answers You Try
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Intermediate Algebra – Student Workbook – Second Edition 2013

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