Unit 2: Graphing Linear Equations and Inequalities

Introduction to Functions Section 1.7 PG 46

Coordinate Plane Vocabulary  2 lines that intersect at a right angle 1. Origin 2. Quadrant 1 (+,+) 3. Quadrant 2 (-, +) 4. Quadrant 3 (-, -) 5. Quadrant 4 (+, -) 6. X axis 7. Y axis

Vocab  Ordered pairs – a pair of #s used to identify a point in a plane  Relation – any set of ordered pairs (x,y)  Input/Domain – collection of all the input values or x- values  Output/Range – collection of all the output values or y- values

Function  a rule that establishes a relationship between 2 quantities (an input and an output).  Each input has one (and only one) output.  More than 1 input can have the same output. f Example: f(x)= x Example: f(x)= x f(2)= f(2)= 5 f(2)= f(2)= 5

You can view anything in the world as a function! Plant Mom

Input-Output Tables  For a relationship to be a function, it must be true that for each input, there is exactly one output.  To make your own input-output table, substitute the given input values into the given equation for x, then solve for y.

Examples  Determine whether each table represents a function. Explain. INPUTOUTPUT INPUTOUTPUT INPUTOUTPUT

Examples  Make an input-output table for the function. Use 0, 1, 2, 3 as the domain. INPUTOUTPUT INPUTOUTPUT INPUTOUTPUT

Keystone Application

CW  Pg. 49 # 1, 2, 4-7

HW  Pg #10-21, 25-26

Functions and Relations Section 4.8 PG 256

Review  A relation is a set of ordered pairs.  The set of all inputs or x-coordinates is called the Domain.  The set of all the outputs or y-coordinates is called the Range.  In order for a relation to be a function, every input (x- value) must correspond with exactly one output (y-value)

Examples  Decide whether the relation shown is a function. If it is, give the domain and range. Input Output Input Output Input Output ) Is the set of ordered pairs {(-4,1 ) (-3,2 ) ( -2,5) ( -1,1)} a function? InputOutput

Vertical Line Test  Used to determine whether or not a graph represents a function.  A graph represents a function if and only if no vertical line passes through two or more points on the graph. More Info...

Vertical Line Test

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Function Notation  The symbol f(x) replaces y  Stands for “the value of f at x”  Can be read simply as “f of x ”  You may also see g( x), h( x), etc. used instead of f(x )

Examples: Evaluate the function for the given value of the variable.

Examples:

CW  Pg 259 #1, 3-9

HW  Pg #11-19 all evens