Functions and Function Notation PDF

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Math 100...

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Math100 Functions and Function Notation  

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“If I know one quantity, can I then determine the other?” o Input/output What is a function? o A rule for a relationship between an input, or independent, quantity and an output, or dependent, quantity in which each input value uniquely determines on output value.  Height and Age  Given a person’s age and trying to determine their height is easy  Given a person’s height and trying to determine their age poses problems o Age uniquely determines height, but not the other way around o Thus, height is a function of age, but age is not a function of height  Items and Prices on a menu  Is price a function of the item? Is the item a function of the price? o Price is a function of item o Item is a function of price only if each item has a different price  Overall percentage you earn in the course corresponds to a grade point  Does grade point a function of percentage? Is percentage a function of grade point? o Grade point is a function of percentage, but percentage is not a function of grade point  “the output is a function of the input” o One-to-One Function  A relationship where each input corresponds to exactly one output, and one output corresponds to exactly one input Function Notation o Height is a function of age

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Which of the tables describes a function?

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Graphs as Functions

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o Vertical Line Test  If you draw a vertical line through a graph and cross two lines, it is not a function o Horizontal Line Test  If you draw a horizontal line through a graph and cross two lines, it is a function but not one-to-one Formulas as Functions

Basic Toolkit Functions...