p. 67

Assignment
• Pp. 71-72 #5-48 all

• A relation is a mapping, or pairing, of input values with output values.
• The set of input values is called the
domain.
• The set of output values is called the
range.
• A relation as a function provided there is exactly one output for each input.
• It is NOT a function if at least one input has more than one output

Identify the Domain and Range. Then tell if the relation is a function.
Input
-3
1
4
Output
-2
3
1
4
Domain = {-3, 1,4}
Range = {3,-2,1,4}
Notice the set notation!!!
No: input 1 is mapped onto
Both -2 & 1

Identify the Domain and Range. Then tell if the relation is a function.
Input
-3
1
3
4
Output
3
1
-2
Domain = {-3, 1,3,4}
Range = {3,1,-2}
Function?
Yes: each input is mapped onto exactly one output

A Relation can be represented by a set of ordered pairs of the form (x,y)
Quadrant II
X<0, y>0
Quadrant I
X>0, y>0
Quadrant III
X<0, y<0
Origin (0,0)
Quadrant IV
X>0, y<0

• To graph the relation in the previous example:
• Write as ordered pairs
(-3,3), (1,-2), (1,1), (4,4)
• Plot the points

(-3,3)
(4,4)
(1,1)
(1,-2)

Same with the points (-3,3),
(1,1), (3,1), (4,-2)

(-3,3)
(1,1)
(3,1)
(4,-2)

Vertical Line Test
• You can use the vertical line test to visually determine if a relation is a function.
• Slide any vertical line (pencil) across the graph to see if any two points lie on the same vertical line.
• If there are not two points on the same vertical line then the relation is a function .
• If there are two points on the same vertical line then the relation is NOT a function

Use the vertical line test to visually check if the relation is a function.
(-3,3)
(4,4)
(1,1)
(1,-2)
Function?
No, Two points are on
The same vertical line.

Use the vertical line test to visually check if the relation is a function.
(-3,3)
(1,1)
(3,1)
(4,-2)
Function?
Yes, no two points are on the same vertical line

Graphing and Evaluating Functions
• Many functions can be represented by an equation in 2 variables: y=2x-7
• An ordered pair is a solution if the equation is true when the values of x & y are substituted into the equation.
• Ex: (2,-3) is a solution of y=2x-7 because:
• -3 = 2(2) – 7
• -3 = 4 – 7
• -3 = -3

• In an equation, the input variable is called the independent variable .
• The output variable is called the dependent variable and depends on the value of the input variable.
• In y=2x-7 ….. X is the independent var.
Y is the dependant var.
• The graph of an equation in 2 variables is the collection of all points (x,y) whose coordinates are solutions of the equation.

Graphing an equation in 2 variables
1. Construct a
2. Graph enough solutions to recognize a pattern
3. Connect the points with a line or curve

Graph: y = x + 1
Step 1
Table of values

Function Notation
• By naming the function ‘f’ you can write the function notation :
f(x) = mx + b
• “the value of f at x”
• “f of x”
• f(x) is another name for y (grown up name)
• You can use other letters for f, like g or h

Decide if the function is linear. Then evaluate for x = -2
• f(x) = -x 2 – 3x + 5
• Not linear….
• f(-2) = -(-2) 2 – 3(-2) + 5
• f(-2) = 7
• g(x) = 2x + 6
• Is linear because x is to the first power
• g(-2) = 2(-2) + 6
• g(-2) = 2
• The domain for both is…..
• All reals