6 4 Absolute Value And Graphing
- 1. Absolute Value and Graphing Review of Chapter 6.4 Pages 295-297
- 2. What’s the Deal? In this lesson We will review domain and range. We will graph the results of how absolute value affects variables.
- 3. 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
- 4. 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)
- 5. 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
- 6. 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….}
- 7. 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
- 8. Graph the points Add a line x y -4 -9 -2 -5 0 -1 +2 3 +4 7
- 9. 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
- 10. 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
- 11. 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
- 12. 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}
- 13. 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
- 14. Absolute Value Equations with Inequalities Key: Split the equation into two parts, a positive and negative side.
- 15. 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:
- 16. 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
- 17. 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
- 18. 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. Solve for negative answer.
- 19. 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.
- 20. 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 Give both answers.
- 21. 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
- 22. 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
- 23. 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
- 24. 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
- 25. Graph the solution to the equation. -14 -12 -10 -8 -6 +4 -2 0 +2
- 26. 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
- 27. Graph the solution to |x - 6| > 5 -4 -2 0 2 4 6 8 10 12
- 28. Extras for presentation x y -4 -2 0 +2 +4 -6 -4 -2 0 +2 +4 +6