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CALCULUS 1 – Algebra review Intervals and Interval Notation.

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Presentation on theme: "CALCULUS 1 – Algebra review Intervals and Interval Notation."— Presentation transcript:

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. ( 3, 7 )- this interval would include all numbers between 3 and 7, but NOT 3 or 7. Round bracket – go up to but do not include this number in the set

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. Square bracket – include this number in the set ( 3, 7 )- this interval would include all numbers between 3 and 7, but NOT 3 or 7. Round bracket – go up to but do not 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. Square bracket – include this number in the set ( 3, 7 )- this interval would include all numbers between 3 and 7, but NOT 3 or 7. Round bracket – go up to but do not 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 ( )

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

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

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

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

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

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

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

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

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

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

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

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 interval


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