|Course:||Michigan Algebra II Preview 2012|
|Printed by:||Guest user|
|Date:||Sunday, July 5, 2020, 03:03 AM|
Table of contents
Since logarithms and exponentials are inverse functions, the graphs will follow the inverse function rules. When graphing logarithmic functions, the values of x and y switch. Therefore, the graphs are reflections across the line y = x.
Typically, when graphing a new function, it is easiest to start with a table of values. Unfortunately for logarithmic functions, it is difficult to select input values and much easier to look at the inverse function.
Graph the function
Step 1. Switch the values of x and y and transform the log to exponential form.
Step 2. Make a table of values for the exponential function.
Step 3. The table above is the inverse of the one needed so switch the input and output. This will create a set of ordered pairs that models the function .
Step 4. Graph the function.
Step 5. State the Domain & Range.
The x-values are approaching an asymptote at x = 0 and the y-values can be any number.
TransformationsThe transformations of functions that were presented in the Families of Functions unit also apply to logarithmic functions. The following list shows how the patterns apply to logarithms.
To learn how to graph log functions, select the following link:Graphing Logarithmic Functions
Interactive ActivityGraphing Logarithmic and Exponential Functions
To solidify your understanding of transformations of logarithmic and exponential graphs, visit the following link to Holt, Rinehart, and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.
PracticeGraphing Log Functions Worksheet
Answer KeyGraphing Log Functions Answer Key
Sources used in this book:
"Graphing Logarithms and Exponentials." http://www.ltcconline.net/greenl/java/IntermedCollegeAlgebra/LogGra ph/logGraph.html (accessed 7/13/2010).
Holt, Rinehart & Winston, "Exponential and Logarithmic Functions." http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch 07_07_homeworkhelp.html (accessed 7/13/2010).
Holt, Rinehart & Winston, "Transforming Logarithmic Functions." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg2/player.ht ml?contentSrc=7158/7158.xml (accessed 7/13/2010).
Embracing Mathematics, Assessment & Technology in High Schools; a Michigan Mathematics & Science Partnership Grant Project