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Lesson 1.6 - …or what is a so rational about these functions?

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Mini-Quiz #2Lesson 1.6 Rational FunctionsLesson 1.6. . . or what is a so rational about these functions?Jeff MeyerJanuary 20, 2009Jeff Meyer Math 115 - Section 13Mini-Quiz #2Lesson 1.6 Rational FunctionsOutline1 Mini-Quiz #22 Lesson 1.6 Rational FunctionsJeff Meyer Math 115 - Section 13Mini-Quiz #2Lesson 1.6 Rational FunctionsMini-Quiz #2QuestionState whether each of the following is odd, even, or neither.21 x12x132x14 x +x15 x +2xJeff Meyer Math 115 - Section 13Mini-Quiz #2Lesson 1.6 Rational FunctionsMini-Quiz #2QuestionState whether each of the following is odd, even, or neither.21 x Even12 Oddx13 Even2x14 x + Oddx15 x + Neither2xJeff Meyer Math 115 - Section 13Mini-Quiz #2Lesson 1.6 Rational FunctionsRecall From Last TimeGoal of Chapter 1(Re-)Introduce basic functions and their propertiesBig Ideas From Last ClassIntroduced the concepts of sine, cosine, and tangentfunctions.Emphasized going between verbal, symbolic, andgraphical descriptions.Jeff Meyer Math 115 - Section 13Mini-Quiz #2Lesson 1.6 Rational FunctionsRecall From Last TimeGoal of Chapter 1(Re-)Introduce basic functions and their propertiesBig Ideas From Last ClassIntroduced the concepts of sine, cosine, and tangentfunctions.Emphasized going between verbal, symbolic, andgraphical descriptions.Jeff Meyer Math 115 - Section 13Mini-Quiz #2Lesson 1.6 Rational FunctionsAlgebraically building functions fromxBuild functions using only ...
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Lesson 1.6
Jeff Meyer
. . . or what is a so rational about these functions?
January 20, 2009
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Lesson 1.6 Rational
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Mini-Quiz #2
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Outline
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Question State whether each of the following is odd, even, or neither. 1x2 1 2 x 1 3 x2 1 4x+ x 1 5x+x2
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Question State whether each of the following is odd, even, or neither. 1x2Even 1 2 x 1 3 x2 1 4x+ x 1 5x+x2
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Goal of Chapter 1 (Re-)Introduce basic functions and their properties
Big Ideas From Last Class Introduced the concepts of sine, cosine, and tangent functions. Emphasized going between verbal, symbolic, and graphical descriptions.
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Big Ideas From Last Class Introduced the concepts of sine, cosine, and tangent functions. Emphasized going between verbal, symbolic, and graphical descriptions.
Goal of Chapter 1 (Re-)Introduce basic functions and their properties
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Terminology Letfbe a polynomial function. The largest natural number for whichanis not zero is the DEGREEoff.
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Definition (Multiply) A POWERFUNCTIONis a function of the form f(x) =axkfor constantsa,k (Add) A POLYNOMIALFUNCTIONis a function of the form f(x) =anxn+an1xn1+∙ ∙ ∙+a1x+a0for constants an,an1, . . . ,a0and natual numbers 1,2, . . .n. (Divide) A RATIONALFUNCTIONis a function of the form gf((xx))wheref(x)andg(x)are polynomial functions.
Build functions using only algebraic operations onx
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Definition (Multiply) A POWERFUNCTIONis a function of the form f(x) =axkfor constantsa,k (Add) A POLYNOMIALFUNCTIONis a function of the form f(x) =anxn+an1xn1+∙ ∙ ∙+a1x+a0for constants an,an1, . . . ,a0and natual numbers 1,2, . . .n. (Divide) A RATIONALFUNCTIONis a function of the form gf((xx))wheref(x)andg(x)are polynomial functions.
Build functions using only algebraic operations onx
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Terminology Letfbe a polynomial function. The largest natural number for whichanis not zero is the DEGREEoff.
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Terminology Letfbe a polynomial function. The largest natural number for whichanis not zero is the DEGREEoff.
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Definition (Multiply) A POWERFUNCTIONis a function of the form f(x) =axkfor constantsa,k (Add) A POLYNOMIALFUNCTIONis a function of the form f(x) =anxn+an1xn1+∙ ∙ ∙+a1x+a0for constants an,an1, . . . ,a0and natual numbers 1,2, . . .n. (Divide) A RATIONALFUNCTIONis a function of the form fg((xx))wheref(x)andg(x)are polynomial functions.
Build functions using only algebraic operations onx
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Terminology Letfbe a polynomial function. The largest natural number for whichanis not zero is the DEGREEoff.
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Build functions using only algebraic operations onx
Definition (Multiply) A POWERFUNCTIONis a function of the form f(x) =axkfor constantsa,k (Add) A POLYNOMIALFUNCTIONis a function of the form f(x) =anxn+an1xn1+∙ ∙ ∙+a1x+a0for constants an,an1, . . . ,a0and natual numbers 1,2, . . .n. (Divide) A RATIONALFUNCTIONis a function of the form fg((xx))wheref(x)andg(x)are polynomial functions.
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What you should get out of lesson. . . Given a rational function, you should be able to determine its Domain. Zeros End behavior.
Note All power functions with natural number exponents are polynomials. All polynomials are rational functions. Do NOT confuse power functionsxkwith exponential functionsax. They have very different properties.
Remarks
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