4-2 Relations and Functions - Math Slide Show

Lesson 4-2
Objective - To represent functions using
models, tables, graphs, and equations.
Function - A rule that describes a dependent
relationship between two quantities.
Domain - The set of input values in a
function.
Range - The set of output values in a
function.
Model:
Let n = #of triangles Let p = the perimeter of each figure
Table: Graph: Equation:
n p Dependent p
8 p = n+2
7
1 3
6
5
Dependent
2 4
4
3
3 5
2 Line is discrete
4 6
1
5 7
0 1 2 3 4 5 6 7 n
6 8
# of triangles
perimeter
Model:
Let n = #of hexagons Let p = perimeter of figure
Table: Graph: Equation:
n p Dependent p
30
p=4n + 2
1 6
25
20
2 10
Dependent
15
3 14
10
Line is discrete
4 18
5
5 22
6 26
perimeter
0 1 2 3 4 5 6 7 n
# of hexagons
A car’s fuel tank is filled at a rate of 1.6 gal/min.
The tank held 5 gallons of gas before refueling.
Let m = #of minutes
Equation:
Let V = Volume of gas in tank V = 5 + 1.6m
Table:
30
Graph:
m V
25
0 5 Volume
20
2 8.2 of gas
15
4 11.4 in tank
10
6
8
14.6
17.8
5 Line is continuous
10 21
0 2 4 6 8 10 12
# minutes
Relation - Any set of ordered pairs
Domain - The set of input values in a function.
Range - The set of output values in a function.
State the domain and range of the relations below.
1) (2, 5), (3, 7), (4, 9), (5, 11)
D=
{ 2, 3, 4, 5}
R = { 5, 7, 9, 11}
2) (-3, 10), (-2, 10), (-1, 6), (1, 6)
D= { −3, −2, −1, 1}
R = { 10, 6}
Relation - Any set of ordered pairs
Function - A type of relation where there
is exactly one output for every input. For
every x there is exactly one y.
x y
x y
1 6
1 6
2 7
2 7
3 7 3
Function
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Lesson 4-2 (cont.)
Relation - Any set of ordered pairs
Function - A type of relation where there
is exactly one output for every input. For
every x there is exactly one y.
x y
x y
1 6
1 7
2 7
1
2
6
7
Not a Function
Function - A rule or equation where there is
exactly one output for every input. For every
x-value there is exactly one y-value.
x y x y
x y
-1 -2 -1 2
1 -2
No x- 0 0 No x- 0 0
0 0
value value x-value
1
repeats
2
4
2
4
6
Yes, it is a
function
1
repeats
2
4
-1
1
2
4
6
2
Yes, it is a
function
repeats
1
2
2 4
4 6
-2
1
2
No, it is not
a function
Determine whether the equation is a function.
y
= x
x = y
x y
-2 2
-1
1
0 0
1 1
2 2
input output
-2 0
-1
0 1
1
2
2
Function
x y
2 -2
1 -1
0 0
1 1
2 2
input output
0 -2
-1
1 0
1
2
2
Not a Function
Tell whether the relation below is a function.
1) input output 3) input output
0
-2
1
3
5 Function
2
-1 Function
4
3
0
2) x y
4)
-3 -1
-3 0
Not a
-3 1 Function
-3 2
input output
-2 3
4
-1
5
0 6
Not a
Function
Vertical Line Test - Functions
Vertical Line Test - Functions
y
y
y
y
y
y
y
y
x
x
x
x
x
x
x
x
Function
y
y
y
y
y
y
y
y
x
x
x
x
x
x
x
x
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Lesson 4-2 (cont.)
Vertical Line Test - Functions
Vertical Line Test - Functions
y
y
y
y
y
y
y
y
x
x
x
x
x
x
x
x
Function
Function
Function Function Not a
Function
y
y
y
y
y
y
y
y
x
x
x
x
x
x
x
x
Vertical Line Test - Functions
Vertical Line Test - Functions
y
y
y
y
y
y
y
y
x
x
x
x
x
x
x
x
Function Function Not a Function
Function
Function Function Not a Function
Function
y
y
y
y
y
y
y
y
x
x
x
x
x
x
x
x
Not a
Function
Function
Not a
Function
Not a
Function
Tell whether the relation below is a function.
1) input output 3) y
3
4
7
x
Function
5
8
6
2) 4) input output
y
5 -1
x
-2
6
Function
-3
7 -4
Not a
Function
Not a
Function
State the domain and range of each function below.
y
y
1)
3)
D: { −2, −1, 2, 4}
R : { −3, 3 1, 2
}
y
2)
x
x
x y
-2 1
-1 -3
2 2
4 2
D:{ x∈ Reals}
R:{ y≥−3}
D:{ −2≤x ≤2}
R :{ { − 1 ≤ y ≤
3
}
y
4)
D:{ x ≥−2}
R:{ y≥
0}
x
x
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010