Download presentation

Presentation is loading. Please wait.

Published byKristopher Gorney Modified over 3 years ago

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 ≥ -1 3- 1

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 - 3- 4 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 - 3- 4 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 - 3- 4 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

Similar presentations

OK

Day Problems For each solution write and graph an inequality.

Day Problems For each solution write and graph an inequality.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on 555 timer circuits Ppt on abo blood grouping antigens Ppt on steps Ppt on non biodegradable wastes Eat before dentist appt on saturday Ppt on payroll in tally Ppt on alternative sources of energy can save this earth Ppt on waves tides and ocean currents definition Ppt on indian army weapons systems Avian anatomy and physiology ppt on cells