logging in or signing up Intro to Graphing Logs wfelton Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 34 Category: Education License: Some Rights Reserved Like it (0) Dislike it (0) Added: April 25, 2011 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Chapter Introduction: Chapter Introduction Exponential Functions How do we solve a x = b? How do we graph f(x)=a x ? What are the properties of logarithms? How do we simplify logarithms? How do we solve logarithms?Reminder of Transformations: Reminder of Transformations What does each of these transformations do to f(x)? f(x)+k Move the function up k. f(x+h) Move the function left h. f(-x) Reflect the function across the y axis f -1 (x) Reflects the function over the y=x line.Here is a graph of f(x)=2x: Here is a graph of f(x)=2 xTransformations: Transformations If f(x)=2 x graph… f(x)+3 f(x+3) f(-x) f -1 (x) Uhhh, how do we do that?Inverse of an exponential function: Inverse of an exponential function If f(x)=2 x The inverse of f(x) is not Remember that the inverse of multiplication -> division, addition -> subtraction What about exponentiation? The inverse of exponentiation is a logarithm.Graphs: Graphs A graph of 2 x and log 2 (x)First section: First section Before we get into logarithms lets look closer at exponential functions. Graph these functions one at a time . f(x) = 2 x <- almost the parent function. g(x) = .5 x h(x)=2 -x What is happening here?2x: 2 x What happens as x gets very negative? Remember that a negative exponent flips the term to the other side of a fraction. 2 -100 = which is a very small number but still positive What happens as x gets very positive? 2 100 is a huge number: What happens as x gets very negative? is a very large number What happens as x gets very positive? is a very small number but still positive.2-x: 2 -x 2 -x is the same thing as So their graphs are identical. We must be aware of the base that we are dealing with. When the base is greater than 1 and the exponent is positive the function grows to the right When the base is between 0 and 1 it grows to the leftAn obvious question.: An obvious question. What if the base is negative or is between -1 and 0? Try it on your calc. You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
Intro to Graphing Logs wfelton Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 34 Category: Education License: Some Rights Reserved Like it (0) Dislike it (0) Added: April 25, 2011 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Chapter Introduction: Chapter Introduction Exponential Functions How do we solve a x = b? How do we graph f(x)=a x ? What are the properties of logarithms? How do we simplify logarithms? How do we solve logarithms?Reminder of Transformations: Reminder of Transformations What does each of these transformations do to f(x)? f(x)+k Move the function up k. f(x+h) Move the function left h. f(-x) Reflect the function across the y axis f -1 (x) Reflects the function over the y=x line.Here is a graph of f(x)=2x: Here is a graph of f(x)=2 xTransformations: Transformations If f(x)=2 x graph… f(x)+3 f(x+3) f(-x) f -1 (x) Uhhh, how do we do that?Inverse of an exponential function: Inverse of an exponential function If f(x)=2 x The inverse of f(x) is not Remember that the inverse of multiplication -> division, addition -> subtraction What about exponentiation? The inverse of exponentiation is a logarithm.Graphs: Graphs A graph of 2 x and log 2 (x)First section: First section Before we get into logarithms lets look closer at exponential functions. Graph these functions one at a time . f(x) = 2 x <- almost the parent function. g(x) = .5 x h(x)=2 -x What is happening here?2x: 2 x What happens as x gets very negative? Remember that a negative exponent flips the term to the other side of a fraction. 2 -100 = which is a very small number but still positive What happens as x gets very positive? 2 100 is a huge number: What happens as x gets very negative? is a very large number What happens as x gets very positive? is a very small number but still positive.2-x: 2 -x 2 -x is the same thing as So their graphs are identical. We must be aware of the base that we are dealing with. When the base is greater than 1 and the exponent is positive the function grows to the right When the base is between 0 and 1 it grows to the leftAn obvious question.: An obvious question. What if the base is negative or is between -1 and 0? Try it on your calc.