3.2 Functions.

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Presentation transcript:

3.2 Functions

Functions Relation: any set of ordered pairs (x, y) Domain: set of x-values Range: set of y-values Function: relation where x-values don’t repeat On a graph, it passes the vertical line test Written:

Ex 1) Relation: {(–1, 0), (0, –1), (1, 0)} Domain: { –1, 0, 1} Range: { –1, 0} Function? YES! (x’s don’t repeat) Ex 2) Is the relation a function? p = {(x, y) │ x = –2} No! Fails vertical line test! Don’t repeat yourself!

Finding the domain & range of an equation: Domain: look for any restrictions on x (y must be real) x under radical x in denominator of fraction

Finding the domain & range of an equation: Range: look for any restrictions on y (using known domain) Draw a quick sketch if need to or use graphing calculator

Ex 3) Find domain & range of Range: y is only positive (square of negative is positive) All Real Numbers Interval Notation:

Ex 4) Find D & R of Domain: term under radical must be ≥ 0 Range: under radical ≥ 0

Find: Ex 5) Ex 6) Ex 7) Ex 8)

Homework #303 Pg. 178 1 – 43 odd