Lesson 1-Analyzing Functions.ppt

Lesson 1-Analyzing Functions.ppt - PRECALCULUS Lesson 1...

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PRECALCULUS Lesson 1: Analyzing Functions
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Today’s Plan Mathematical Modeling Numerical/Algebraic/Graphical Models Zero Factor Property A caution about graphing utilities Functions Definition/Notation Domain & Range Increasing/Decreasing Boundedness Extrema Symmetry Asymptotes/End behavior Homework 1
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Mathematical Modeling A mathematical model uses a mathematical structure to approximate real world phenomena for the purpose of studying or predicting their behavior. See Section 1.1 for examples. A numerical model analyzes numbers (data) to gain insight into phenomena. This is your basic data chart or table. An algebraic model uses formulas to relate variable quantities associated with the phenomena being studied. This model can be used to generate numerical values of unknown quantities by relating them to known quantities. A graphical model is a visual representation that gives insight into the relationships between variable quantities. Each model type is useful for different types of phenomena, and insights can often be gained by switching from one kind of model to another. We will be utilizing all of these models throughout the course.
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The Zero Product Property The Zero Product Property (or Zero Factor Property, or Multiplicative Property of Zero) is a very useful mathematical property. It states that if a product is equal to zero, then one or more of its factors must be zero. If ab = 0, then a = 0 or b = 0. This property allows us to solve equations of one variable by setting the equation equal to zero and factoring. x x x 20 8 2 3
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Graphing Calculators Uses Limitations
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Relations A relation is a relationship between two sets of information. The elements in one set get mapped onto the elements in the second set. For instance, we could map each student in the room with their desk location.
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