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3.1

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3.1

1. 1. FUNCTIONs 3.1
2. 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. 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. 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. 5. Types of Function “Rules”
6. 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?
7. 7. 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
8. 8. 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]