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

Jeff Meyer

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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 ...

Informations

• Publié par: Abbu
• Nombre de lectures: 27
• Langue: English

Extrait

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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

Functions

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Outline

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Question State whether each of the following is odd, even, or neither. 1 x 2 1 2 x 1 3 x 2 1 4 x+ x 1 5 x+ x 2

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Question State whether each of the following is odd, even, or neither. 1 x 2 Even 1 2 x 1 3 x 2 1 4 x+ x 1 5 x+ x 2

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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 whicha n is not zero is the D EGREE off.

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Definition (Multiply) A P OWER F UNCTION is a function of the form f(x) =ax k for constantsa,k (Add) A P OLYNOMIAL F UNCTION is a function of the form f(x) =a n x n +a n−1 x n−1 +∙ ∙ ∙+a 1 x+a 0 for constants a n ,a n−1 , . . . ,a 0 and natual numbers 1,2, . . .n. (Divide) A R ATIONAL F UNCTION is a function of the form g f ( ( x x ) ) wheref(x)andg(x)are polynomial functions.

Build functions using only algebraic operations onx

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Definition (Multiply) A P OWER F UNCTION is a function of the form f(x) =ax k for constantsa,k (Add) A P OLYNOMIAL F UNCTION is a function of the form f(x) =a n x n +a n−1 x n−1 +∙ ∙ ∙+a 1 x+a 0 for constants a n ,a n−1 , . . . ,a 0 and natual numbers 1,2, . . .n. (Divide) A R ATIONAL F UNCTION is a function of the form g f ( (x x ) ) 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 whicha n is not zero is the D EGREE off.

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Terminology Letfbe a polynomial function. The largest natural number for whicha n is not zero is the D EGREE off.

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Definition (Multiply) A P OWER F UNCTION is a function of the form f(x) =ax k for constantsa,k (Add) A P OLYNOMIAL F UNCTION is a function of the form f(x) =a n x n +a n−1 x n−1 +∙ ∙ ∙+a 1 x+a 0 for constants a n ,a n−1 , . . . ,a 0 and natual numbers 1,2, . . .n. (Divide) A R ATIONAL F UNCTION is a function of the form f g ( ( x x ) ) 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 whicha n is not zero is the D EGREE off.

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Build functions using only algebraic operations onx

Definition (Multiply) A P OWER F UNCTION is a function of the form f(x) =ax k for constantsa,k (Add) A P OLYNOMIAL F UNCTION is a function of the form f(x) =a n x n +a n−1 x n−1 +∙ ∙ ∙+a 1 x+a 0 for constants a n ,a n−1 , . . . ,a 0 and natual numbers 1,2, . . .n. (Divide) A R ATIONAL F UNCTION is a function of the form f g ( (x x ) ) 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 functionsx k with exponential functionsa x . They have very different properties.

Remarks

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