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  • chapter-1-Functions and Models

    • Four ways to represent afunction
      Definitions: Function, Domain and Range of (Polynomial of first and second degree),
       Representation of Functions and their Graphs,
      The Vertical Line Test, Piecewise Defined Functions, 
      Symmetry (Odd & Even) Functions.

    • Mathematical Models: A
      Catalog of Essential Functions
      Essential Functions: Polynomial, Power, Rational, Algebraic,
      Trigonometric, Exponential, and Logarithmic.
      Families of Essential Functions and Their Graphs.(must know)


    • New Functions from Old Functions
      Transformations of Functions:
       i) Vertical and Horizontal Shifts.
       ii) Vertical and Horizontal Reflecting,
       Combination of Functions (f(+,-)g), f.g, f/g,
       And Composite Functions) and their Domains


    • Exponential Functions
      Exponential Function and Their Graphs
      Laws of Exponents
      The Number e.


    • Inverse Functions and Logarithms
      Inverse Functions: Definitions  
       Horizontal Line Test;
      Logarithmic Functions: Definitions
      Laws of Logarithms,
      Natural Logarithm: formulas
      Inverse Trigonometric Functions and their cancellation equations:
       (𝐲 = 𝐬𝐢𝐧−𝟏𝐱, 𝐲= 𝐜𝐨𝐬−𝟏𝐱, 𝐲 = 𝐭𝐚𝐧−𝟏𝐱 only),
       Identify the graphs of a function and it’s inverse if they are given on the same axes.