Integrated Math 1 Notes

​Chapter​​1​

,​1.1.1​
​Absolute​​Value​

​ bsolute​​value​​is​​the​​numerical​​value​​of​​a​​number​​without​​its​​sign.​ ​The​​symbol​​for​
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​absolute​​value​​is​​two​​vertical​​bars,​| |​.​ ​Absolute​​value​​can​​represent​​the​​distance​​on​​a​
​number​​line​​between​​a​​number​​and​​0.​​Since​​a​​distance​​is​​always​​positive,​​the​​absolute​
​value​​is​​always​​either​​a​​positive​​value​​or​​0.​​The​​absolute​​value​​of​​a​​number​​is​​never​
​negative.​

​ or​​example,​​the​​number​​-3​​is​​3​​units​​away​​from​​0,​​as​​shown​​on​​the​​number​​line​​at​​right.​
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​Therefore,​​the​​absolute​​value​​of​​–3​​is​​3.​ ​This​​is​​written​|− ​3|​ = ​3​.​




​ ikewise,​​the​​number​​5​​is​​5​​units​​away​​from​​0.​ ​The​​absolute​​value​​of​​5​​is​​5,​​written​
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|​5|​ = ​5​.​

,​1.1.2​
​Families​​of​​Functions​

​Functions​​can​​be​​categorized​​into​​“families”.​

​ ne​​family​​of​​functions​​is​​the​​linear​​functions​​.​ ​Linear​​functions​​have​​a​​graph​​that​​is​​a​
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​straight​​line.​ ​The​​line​​may​​or​​may​​not​​pass​​through​​the​​origin,​​and​​it​​may​​be​​increasing​
​or​​decreasing​​from​​left​​to​​right.​

​ nother​​function​​family​​is​​called​​direct​​variation​​(also​
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​called​​direct​​proportion​​or​​proportional​​),​​which​​is​​a​​linear​
​function​​that​​passes​​through​​the​​origin.​ ​It,​​too,​​may​​be​
​increasing​​or​​decreasing​​from​​left​​to​​right.​ ​The​​data​​you​
​gathered​​in​​the​​“Sign​​on​​the​​Dotted​​Line”​​lab​​(in​​problem​
​1-11)​​is​​an​​example​​of​​an​​increasing​​proportion.​ ​In​​a​
​proportional​​situation,​​if​​the​​x-value​​is​​doubled​​(or​​tripled),​
​the​​y-value​​is​​also​​doubled​​(or​​tripled).​

​ n​​example​​of​​a​​decreasing​​proportion​​is​​the​​elevation​​of​​a​
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​submarine​​as​​it​​is​​descending.​

​ nother​​function​​is​​inverse​​variation​​(also​​called​​inverse​
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​proportion​​).​ ​The​​data​​collected​​in​​the​​“Hot​​Tub​​Design”​​lab​
​(in​​problem​​1-11)​​is​​an​​example​​of​​inverse​​variation.​

​ ou​​also​​observed​​an​​exponential​​function​​.​ ​The​​growth​​of​
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​infected​​people​​in​​the​​“Flu​​Epidemic”​​(in​​problem​​1-11)​​was​
​exponential.​

​ e​​will​​define​​what​​a​​function​​is​​later​​in​​this​​chapter.​ ​We​​will​
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​develop​​linear​​functions​​and​​exponential​​functions​​in​​much​
​more​​depth​​later​​in​​this​​course.​

, ​1.1.3​
​Types​​of​​Angles​

​ hen​​trying​​to​​describe​​shapes,​​it​​is​​convenient​​to​
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​classify​​types​​of​​angles.​ ​An​​angle​​is​​formed​​by​​two​​rays​
​joined​​at​​a​​common​​endpoint,​​called​​a​​vertex.​ ​The​
​measure​​of​​an​​angle​​represents​​the​​number​​of​​degrees​​of​
​rotation​​from​​one​​ray​​to​​the​​other​​about​​the​​vertex.​ ​This​
​course​​will​​use​​the​​following​​terms​​to​​refer​​to​​angles:​

​ cute​​Angle:​​Any​​angle​​with​​measure​​between​​(but​​not​
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​including)​​0º​​and​​90º.​




​Right​​Angle:​​Any​​angle​​that​​measures​​90º.​




​ btuse​​Angle:​​Any​​angle​​with​​measure​​between​ ​(but​​not​
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​including)​​90º​​and​​180​​º.​




​ traight​​Angle:​​Straight​​angles​​have​​a​​measure​​of​​180º​​and​​are​
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​formed​​when​​the​​sides​​of​​the​​angle​​form​​a​​straight​​line.​

​Circular​​Angle:​​Any​​angle​​that​​measures​​360º.​