  Graphs

2.1 Graphs

Need To Know Review Coordinate System Graphing Equations

Coordinate System Vocabulary X-axis Y-axis Ordered Pair (x, y) Origin (0,0) Quadrants I, II, III, IV Examples: Plot (3, 4), (–2, 0), (4.5, –2) (–1, –5 ) Solutions of Equations

 If an equation has two variables, 1. A solution is a pair 2. There are infinite solutions 3. Order matters 4. Generally, alphabetic order Example Determine whether (2, 5) and (–2, 1) are solutions to y = 2x + 1.

Graphing Equations

 An equation whose graph is a straight line is a linear equation . First power x and first power y. Plot 3 points Many equations graph are not straight lines. These equations are called nonlinear equations. Higher power on x or y or some special function.Plot 5 to 7 points or more. Several points are necessary because the graph curves or changes . You’ll need extra points to see where those changes occur .

Graphing Linear Equations

 Graph: y = 3x + 21. Choose x 2. Compute y 3. Plot pair 4 3 pairs 5. Connect Dots Graphing Non- Linear Equations

 Graph:  Graph:  2.2 Functions

Need To Know Functions Definition Notation Graphing Vertical Line test

Function Vocabulary

A _________ is a matching or pairing of things,
generally numbers .

Ex: People in class paired with their favorite color.

A ________ is a relation where every domain
element (x thing) is paired to only one range
element (y thing). Function Examples

A function is a relation where every domain element
(x thing) is paired to only one range element (y thing).

Are these functions?

 Domain Range Domain Range  Function Notation Examples:

 f(x) = x + 2 Evaluate f(-3) g(n) = 3n2 – 5 Evaluate g(-2)

Function Example

 Find f(1) Domain, Range, x-valure for f(x) = 1 Find f(1) Domain, Range, x-valure for f(x) = 1 Find f(1) Domain, Range, x-valure for f(x) = 1 Vertical Line Test

When can a picture of a graph be a function?
Vertical Line Test – Prev Next

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