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Functions

Functions. Section 3.8. Multiple Choice. A function is a correspondence between a first set, called the domain and a second set, called the range, such that each member of the domain corresponds to __________ member of the range. A. At least one B. Exactly one C. None of the above .

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Functions

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  1. Functions Section 3.8

  2. Multiple Choice • A function is a correspondence between a first set, called the domain and a second set, called the range, such that each member of the domain corresponds to __________ member of the range. • A. At least one • B. Exactly one • C. None of the above

  3. Overview • Functions and Graphs • Function Notation and Equations • Functions Defined Piecewise • Linear Functions and Applications

  4. Functions • Function – Correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to exactly one member of the range DOMAIN RANGE CORRESPONDENCE Example: To each person in class There corresponds A date of birth To each bar code at Home Depot A price There corresponds To each real number There corresponds The cube of that number

  5. DOMAIN: Founding Fathers CORRESPONDENCE: When that person signed the Declaration of Independence Functions RANGE: A set of dates John Hancock Aug 2, 1776 Thomas McKean 1781 John Witherspoon Thomas Jefferson John Adams

  6. DOMAIN: Founding Fathers RANGE: A set of dates Functions CORRESPONDENCE: When they died John Hancock Oct 8, 1793 Thomas McKean June 24, 1817 John Witherspoon Nov 15, 1794 Thomas Jefferson July 4, 1826 John Adams

  7. Washington Oregon Idaho Kansas Montana N. Dakota Nebraska Wyoming Nevada Willow Goldfinch Western Meadowlark Mountain Bluebird What is the Correspondence?

  8. Washington, My Home Here We Have Idaho Oregon, My Oregon My Homeland Tennessee When It’s Iris Time in Tennessee My Tennessee The Tennessee Waltz Rocky Top Tennessee Washington Idaho Oregon Tennessee What is the Correspondence?

  9. 1 2 3 4 5 2 3 4 5 6 What is the Correspondence?

  10. 1 2 3 4 5 2 4 6 8 10 What is the Correspondence?

  11. 1 2 3 4 5 1 4 9 16 25 What is the Correspondence?

  12. Functions and Graphs • Functions can be expressed as ordered pairs • See graph on p 255 • Function is written as {(-3, 5), (1,2), (4,2)} • Domain is {-3, 1, 4} • Range is {5, 2} • Functions generally represented by lower or upper case letters • Abbreviation for real numbers • Closed dot indicates that point is on the graph • Open dot indicates point is not on graph

  13. Functions and Graphs • If graph has two or more points with same first coordinate, then NOT a graph of a function • Vertical line test • Even if not a function, graph still represents relations • Relation is a correspondence between domain and range, such that each member of domain corresponds to a least one member of the range

  14. Function Notations and Equations • Element of domain is the input and the corresponding element of the range is output • Function notation – f(x) • “f of x” or “f at x” or “the value of f at x” • x is the input and f(x) is the output • It does not mean f times x • Often used in formulas

  15. Functions Defined Piecewise • Different equations for different parts of the domain

  16. Linear Functions and Applications • Linear function is any nonvertical line that passes vertical-line test and is the graph of a function • f(x) = mx + b

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