1.2 - Mathematical Models: A Catalog of Essential Functions.

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Presentation transcript:

1.2 - Mathematical Models: A Catalog of Essential Functions

Mathematical Models Mathematical models are mathematical descriptions of real-world phenomenon.

Essential Functions _______________ Function Includes: Constant, Linear, Quadratic, Functions. Facts: n must be an __________________. Cannot have variables in denominators or in radicands of roots.

Essential Functions _________________ Functions where c is a constant and a is any real number (usually rational). Includes: Some Polynomial, Root, and Reciprocal Functions, but must have only ______ term(s).

Essential Functions ________________ Functions where P(x) and Q(x) are _________ functions. Facts: Cannot have any radicals with variables in the radicand.

Essential Functions ________________ Functions

Essential Functions Algebraic Functions Algebraic Functions are any function constructed using mathematical operations.

Essential Functions Trigonometric Functions Trigonometric functions tend to be periodic in nature (repeating the same patterns in a predictable manner).

Essential Functions Exponential Functions where b _____ and b _____.

Essential Functions __________________ Functions where b ____ and b ____. Logarithmic functions are the inverses of exponential functions (and vice versa).

Essential Functions Transcendental Functions Transcendental functions include the trigonometric, inverse trigonometric, exponential, and logarithmic functions, but also includes a vast number of other functions that have never been named.

Example: Classify each function. Some may be more than one type.