Solving & Graphing Absolute Values on Number Line
Absolute value inequalities, geometric definition of absolute value, solutions to inequalities, graphical representations, and shifts on the number line. Learn to interpret and graph solutions to various absolute value equations and inequalities with clear visual examples.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
SOLVING AND GRAPHING ABSOLUTE VALUES ON A NUMBER LINE
THE GEOMETRIC DEFINTION OF ABS VALUE The absolute value of a number measures its The absolute value of a number measures its distance to the origin on the real number line. distance to the origin on the real number line. For example: For example: ? =5 Translates into Translates into English: are looking for those real numbers are looking for those real numbers x x whose distance from the origin is distance from the origin is 5 units. X=5 or x= X=5 or x=- -5 5 English: we whose we 5 units.
WHAT ABOUT THE SOLUTIONS TO INEQUALITIES ? < 5 Translate into English: we are looking for those real numbers x whose distance from the origin is less than 5 units. we are talking about values in the interval between -5 and 5: ? < ? < ?
WHAT ABOUT THE SOLUTIONS TO INEQUALITIES ? 2 In English: which numbers, x, are at least 2 units away from the origin? On the left side, real numbers less than or equal to -2 qualify, on the right all real numbers greater than or equal to 2: ? ? ?? ? ?
QUICK SUMMERY If If If ? < ? ???? - -a<x<a a<x<a ? > ? ???? x< x<- -a OR a OR x>a x>a
LOCATOR POINT Think of zero on the number line as the locator point of absolute value. Do you remember how parent graphs shift horizontally? Do you remember how the parent graph shrink or stretch? The same concepts apply to graphing abs values on a number line.
LET'S FIND THE SOLUTIONS TO THE INEQUALITY: Let's find the solutions to the inequality: ? ? ? The locator point has been translated from the zero to 2 2. So the equation above means any points that are 1 unit or less away from 2. 1 ? 3
WHAT ABOUT THE EXAMPLE ? + 1 3 The locator point has shifted 1 unit left. You are looking for points that are 3 or more units away from -1. ? ? ?? ? ?
WHAT ABOUT THE EXAMPLE 2? 6 The locator point has not been shifted. The distance from zero has been reduced by a factor of 2. So you are looking for points that are more than 3 (i.e 6 2) units away from zero. ? ? ?? ? ?
WITH A LITTLE BIT OF TWEAKING, OUR METHOD CAN ALSO HANDLE INEQUALITIES SUCH AS ?? ? < ? Shift 5 units right Shift 5 units right Shrink the distance of 8 by a factor of 2 Shrink the distance of 8 by a factor of 2 Start at 5 and move 4 units in each Start at 5 and move 4 units in each direction: 4+5=9 and 5+ direction: 4+5=9 and 5+- -4=1 4=1 1 < ? < 9
TEST POINT Choose a value of x between -1 and 9. Let s say x=0 ?(?) ? < ? ? < ? 5<8 is true 5<8 is true
CLICK HERE FOR GUIDED PRACTICE PROBLEMS
