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Chapter 1: Functions and Models

A concise collection of lecture notes and summaries on functions

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Co-Ordinate Geometry

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Introduction to and revision on Co-Ordinate Geometry: description of distance midpoint formula; definition and formula of straight lines; formula for parallel and perpendicular lines; formula for circles and graphical representations; also includes worked examples for each section

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Summary New from Old Functions

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Introducing the concept of shifting functions to produce new functions (new from old); how to shift functions; graphical and algebraic representations; combinations of functions algebraically and graphically; compositions of functions and examples

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Inverse Functions

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Introduction to Inverse Functions: Discussion of exponential and logarithmic functions as examples of inverse functions; using Vertical Line Test to check if functions are one-to-one or one-to-many; strategy for finding the inverse function; sketching of inverse functions

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Inequalities

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Providing worked examples of inequalities; introduction to absolute values; relationship between absolute values and inequalities; sketching inequalities and absolute values (graphical representation)

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Summary Functions

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Concise introduction to functions: definition of a function; examples of functions; ways of representing functions; sketching graphs of functions graphically; identifying functions using the Vertical Line Test (VLT)

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