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# 6 4 Absolute Value And Graphing

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## 6 4 Absolute Value And GraphingPresentation Transcript

• Absolute Value and Graphing Review of Chapter 6.4 Pages 295-297
• What’s the Deal?
• In this lesson
• We will review domain and range.
• We will graph the results of how absolute value affects variables.
• y = +7
• Since every y value equals 7, we graph with a zero slope.
• y = (0)x + 7
• Using an x-y box
• (-4, +7)
• (-2, +7)
• ( 0, +7)
• (+2, +7)
• (+4, +7)
x y -4 7 -2 7 0 7 +2 7 +4 7
• y = +7
• Arrows
• Show that all points beyond also make the equation true.
• Using an x-y box
• (-100, +7)
• (-52, +7)
• ( 10, +7)
• (+20, +7)
• (+144, +7)
• What are the domain and range?
• The domain for an equation is all the values that will work for x.
• The range for an equation is all the values that will work for y.
• Domain : {all real numbers}
• Range : {+7}
x y -4 7 -2 7 0 7 +2 7 +4 7
• Number Terms
• Integers {…,-6,-5,-4,-3,-2,-1,0,1,2,3,4…}
• Whole Numbers { 0,1,2,3,4,5,6,7…}
• Counting Numbers { 1,2,3,4,5,6,7…}
• Real Numbers {integers, fractions, decimal numbers, repeating decimals, non-repeating decimals….}
• Task: Graph y = 2 x -1 and find the domain & range
• Once again use and x-y box. (y=mx+b)
• Fill in -4 for x.
• y=2(-4)-1
• y=-8-1
• y= -9
• Do the same for the rest of the values chosen.
-9 When you are finished, go to the next slide. x y -4 -2 0 +2 +4
• Graph the points
x y -4 -9 -2 -5 0 -1 +2 3 +4 7
• Name the domain and range.
• Any number can be used as x or y.
• Domain:{all real numbers}
• Range:{all real numbers}
x y -4 -9 -2 -5 0 -1 +2 3 +4 7
• Graph y = | x-2 |
• Start by using an x-y box with 0 and some negative and positive numbers for x.
• | -5 -2| = |-7|
• |-7| = 7
+7 x y -5 -1 0 +2 +6 +8
• Graph y = | x-2 |
• Show the graphed pairs.
• Fill in a few more values that work.
x y -5 7 -1 3 0 2 +2 0 +6 4 +8 6
• Is y = | x-2 | a linear equation?
• You can begin to see that the values form a V when graphed, not a line.
• Any real number can be used as x, but no negative numbers are used for y.
• Domain:{all real numbers}
• Range:{all wholel numbers}
• How is y = - | x-2 | different?
• All the y values are opposite the previous equation’s y-values.
x y -5 7 -1 3 0 2 +2 0 +6 4 +8 6 x y -5 -7 -1 -3 0 -2 +2 -0 +6 -4 +8 -6
• Absolute Value Equations with Inequalities Key: Split the equation into two parts, a positive and negative side.
• Absolute Value
• To find Absolute value,
• find the solution inside the absolute value signs
• Make that value positive (+)
• Continue on with order of operations outside the signs
• Example:
• Making Use of Absolute Value
• Adding a positive to a negative integer
• Which has the higher absolute value?
• The positive or negative sign of that number is in the answer.
• Now find the difference.
- 13
• Find the value: |x-2| =7
• This has two possible answers.
• There must be a handy pattern to use to find both.
• |+9-2| =7
• |-5-2| =7
• How to find the value: |x-2| =7
• This problem should be done twice.
• Procedure:
• Remove the absolute value signs
• Solve for the positive answer.
• Rewrite without absolute value signs.
• Procedure |x-2| =7
• Remove absolute value signs.
• x - 2 = 7
• Solve for x
• x +2 -2 = +2 + 7
• x = 9
• Make 2 nd equation’s answer negative.
• x - 2 = -7
• Solve for x
• x +2 -2 = +2 - 7
• x = -5
Let’s take another look at a previous slide and see if the answers given were correct.
• Find the value: |x-2| =7
• This has two possible answers.
• There must be a handy pattern to use to find both.
• |+9-2| =7
• |-5-2| =7
• x = -5 OR +9
• Procedure for | x-10 | =4.5
• Remove absolute value signs.
• x - 10 = 4.5
• Solve for x
• x +10 -10 = +10 + 4.5
• x = 14.5
• Make 2 nd equation’s answer negative.
• x - 10 = -4.5
• Solve for x
• x +10 -10 = +10 – 4.5
• x = -5.5
• x = -5.5 OR +14.5
• Solve for | 2 x-14 | = 8
• Part One.
• 2 x - 14 = 8
• +14 +14
• 2x +0 = 22
• x = +11
• Part Two.
• 2 x - 14 = -8
• +14 +14
• 2x +0 = 6
• x = 3
• x = +3 OR +11
• Solve for |x - (-5)|  8
• Part One.
• x + 5  8
• -5 -5
• x +0  3
• x  +3
• Switch the sign for the negative. Why?
• x + 5  -8
• -5 -5
• x +0  -13
• x  -13
• x  -13 OR x  +3
• Graph the solution for |x - (-5)|  8
• You can rewrite the OR statement.
• Then graph.
• x  -13 OR x  +3
• -13  x  +3
-6 -4 -2 0 +2 +4 +6
• Graph the solution to the equation. -14 -12 -10 -8 -6 +4 -2 0 +2
• Solve for |x - 6| > 5
• Part One.
• x - 6 > 5
• +6 +6
• x +0 > 11
• x > +11
• Switch the sign for the negative. Why?
• x - 6 < -5
• +6 +6
• x +0 < +1
• x < +1
• x > +1 OR x < +11
• Graph the solution to |x - 6| > 5 -4 -2 0 2 4 6 8 10 12
• Extras for presentation x y -4 -2 0 +2 +4 -6 -4 -2 0 +2 +4 +6