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CALCULUS 1 – Algebra review

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  1. CALCULUS 1 – Algebra review Intervals and Interval Notation

  2. CALCULUS 1 – Algebra review Intervals and Interval Notation Intervals are sets of real numbers. The notation uses square and round brackets to show these sets of numbers.

  3. CALCULUS 1 – Algebra review Intervals and Interval Notation Intervals are sets of real numbers. The notation uses square and round brackets to show these sets of numbers. Round bracket – go up to but do not include this number in the set

  4. CALCULUS 1 – Algebra review Intervals and Interval Notation Intervals are sets of real numbers. The notation uses square and round brackets to show these sets of numbers. Round bracket – go up to but do not include this number in the set ( 3 , 7 ) - this interval would include all numbers between 3 and 7, but NOT 3 or 7.

  5. CALCULUS 1 – Algebra review Intervals and Interval Notation Intervals are sets of real numbers. The notation uses square and round brackets to show these sets of numbers. Round bracket – go up to but do not include this number in the set ( 3 , 7 ) - this interval would include all numbers between 3 and 7, but NOT 3 or 7. Square bracket – include this number in the set

  6. CALCULUS 1 – Algebra review Intervals and Interval Notation Intervals are sets of real numbers. The notation uses square and round brackets to show these sets of numbers. Round bracket – go up to but do not include this number in the set ( 3 , 7 ) - this interval would include all numbers between 3 and 7, but NOT 3 or 7. Square bracket – include this number in the set [ 3 , 7 ] - this interval would include all numbers from 3 to 7..

  7. CALCULUS 1 – Algebra review Intervals and Interval Notation When working with equations containing an inequality, the symbols for the inequality determine how you graph and represent the solution as an interval. Round bracket -less than ( < ) , greater than ( > )

  8. CALCULUS 1 – Algebra review Intervals and Interval Notation When working with equations containing an inequality, the symbols for the inequality determine how you graph and represent the solution as an interval. Round bracket -less than ( < ) , greater than ( > ) - open circle on a graph

  9. CALCULUS 1 – Algebra review Intervals and Interval Notation When working with equations containing an inequality, the symbols for the inequality determine how you graph and represent the solution as an interval. Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket – less than or equal to ( ≤ ), greater than or equal to ( ≥ )

  10. CALCULUS 1 – Algebra review Intervals and Interval Notation When working with equations containing an inequality, the symbols for the inequality determine how you graph and represent the solution as an interval. Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph

  11. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE : Solve and graph and show your answer as an interval

  12. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE : Solve and graph and show your answer as an interval

  13. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE : Solve and graph and show your answer as an interval graph 4

  14. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE : Solve and graph and show your answer as an interval graph 4 interval

  15. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval

  16. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval

  17. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval - 1 3 This results in two graphs… x < 3 x ≥ -1

  18. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval - 1 3 The solution set is where the two graphs overlap ( share )

  19. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval - 1 3 The solution set is where the two graphs overlap ( share ) [ -1 , 3 ) interval

  20. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 3 : Solve and graph and show your answer as an interval

  21. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval

  22. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval These are our critical points

  23. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval - 4 - 3 These are our critical points Graph the critical points and then use a test point to find “true/false”

  24. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval FALSE TRUE TRUE - 4 - 3 0 TEST x = 0 These are our critical points Graph the critical points and then use a test point to find “true/false”

  25. CALCULUS 1 – Algebra review Intervals and Interval Notation Round bracket - less than ( < ) , greater than ( > ) - open circle on a graph Square bracket - less than or equal to ( ≤ ), greater than or equal to ( ≥ ) - closed circle on a graph EXAMPLE # 2 : Solve and graph and show your answer as an interval FALSE TRUE TRUE - 4 - 3 0 TEST x = 0 interval These are our critical points Graph the critical points and then use a test point to find “true/false”

  26. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart.

  27. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 1 : Solve

  28. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 1 : Solve

  29. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 2 : Solve

  30. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 2 : Solve Remember u substitution from pre-calc ?

  31. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 2 : Solve Remember u substitution from pre-calc ?

  32. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 2 : Solve Remember u substitution from pre-calc ? Can’t have an absolute value equal to a negative answer

  33. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 2 : Solve Remember u substitution from pre-calc ? Now solve the absolute value equation …

  34. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 3 : Solve , and show the solution set as an interval.

  35. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 3 : Solve , and show the solution set as an interval.

  36. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 3 : Solve , and show the solution set as an interval. I like to graph the solution to determine the interval… 4 -1

  37. CALCULUS 1 – Algebra review Absolute Value Equations Remember, absolute value equations have two possible answers; positive and negative. So when solving, drop the absolute value sign, and set the equation equal to the original answer, and also it’s negative counterpart. EXAMPLE # 3 : Solve , and show the solution set as an interval. I like to graph the solution to determine the interval… 4 -1 interval