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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 + 2

1. 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 –

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