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## CALCULUS 1 – Algebra review

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**CALCULUS 1 – Algebra review**Intervals and Interval Notation**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.**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**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.**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**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..**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 ( > )**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**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 ( ≥ )**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**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**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**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**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**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**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**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**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 )**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**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**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**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**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”**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”**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”**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.**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**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**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**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 ?**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 ?**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**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 …**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.**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.**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**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