3.1
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This document defines and provides examples of functions. It discusses the key components of a function including domain, range, and the function notation of f(x). It describes different types of function rules including piecewise functions, greatest integer functions, and restrictions on the domain. Examples are provided to illustrate piecewise functions and the greatest integer function.
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3.1
- 2. Definitions • Relation: a relationship between sets of info – Pairing of names and heights of Precalc students – Data for times and high tides for Hampton VA • Domain: possible values of inputs (typically called “x”) • Range: possible values of outputs (typically called “y”) • Function: a “well-behaved” type of relation – Each input has one and only one output!
- 3. 1 2 3 5 6 7 8 9 1 3 5 7 9 5 7 8 Which is a function? Domain Domain Range Range
- 4. Function Notation Name of function (“f of x”) Input number f(x) = 5x2 +3 Output number Rule, or directions that tell you what to do with the input to produce the output (“square it, multiply it by 5, then add 3 to it”)
- 5. Types of Function “Rules”
- 6. Domain Convention • Unless told otherwise, domain of f is all real number inputs that the rule produces a real number output • Two primary restrictions – Can’t divide by zero – Can’t take the square root of a negative number • Some real-world problems may further restrict the domain – Does negative time or distance make sense?
- 8. Piecewise Functions • The rule includes several formulas • Each formula applies to certain values of the domain • So which rule or formula you apply depends on the input value • What is f(-5)? f(8)? the domain of f? f(x) = 2x +3 if x < 4 x2- 1 if 4 ≤ x ≤ 10
- 9. Greatest Integer Function • For any number x, round down to the nearest integer less than or equal to x • The symbol is a set of brackets • Remember negative numbers round down, which is left on the number line! • This is an example of a step function • TI-83/4: MATH, NUM, 5: int( • What is f(-4.7)? f(-3)? f(0)? f(5/4)? f(π)? f(x) = [x]