�ݺ�ߣ

Determining the
Dependent and
Independent Variables
and Finding the
Domain and Range of a
Function

ACTIVITY 1: THE VARIABLES
Directions: Determine the quantities that change (or
the variables) in each of the following situation. Item
number 1 is done as an example.
1. Rosario is making souvenirs for a friend’s wedding.
The number of invited people to attend the wedding
determines the number of souvenirs she must make.
The variables are:
the number of invited people
the number of souvenirs

Directions: Determine the quantities that
change (or the variables) in each of the following
situation. Item number 1 is done as an example.
2. George is selling brownies
online. The more brownies he sells,
the more money he earns. The
variables are:

Directions: Determine the quantities that change (or
the variables) in each of the following situation. Item
number 1 is done as an example.
3. A bakery in Cabadbaran City sells
different types of bread. The more
bread the customers buy, the more
sacks of flour they will use. The
variables are:

INDEPENDENT VARIABLE
is a variable that will change by taking
on different values. It changes
independently. In a relation,
independent variable controls the
dependent variable. It is generally
represented by the −variable or
𝑥
what is referred to as the −value.
𝑥

DEPENDENT VARIABLE
is a variable that is affected by the
independent variable, and it changes
in response to the independent
variable. In a relation, dependent
variable depends on the independent
variable. It is generally represented by
the −variable or what is referred to
𝑦
as the −value.
𝑦

In the scenario, which must
happen first before the other
occurs? Which variable controls
the other, and which variable
depends on the other?

DOMAIN OF A FUNCTION
is the set of all acceptable inputs.
Generally, domain is the set of 𝑥
−values or the abscissa of the ordered
pairs of a function.

DOMAIN OF A FUNCTION
When represented as ordered pairs is
the set of the first coordinates or it is
the set of all values that can be used
for the independent variable. In the
function y=2/x
The domain is the set of all nonzero
real numbers since 2/x is undefined for
x=0.

RANGE OF A FUNCTION
is the set of resulting outputs.
Generally, range is the set of −values
𝑦
or the ordinate of the ordered pairs of
a function.

RANGE OF A FUNCTION
Is the set of second coordinates or the
set of all values of the dependent
variables.

Defn: A relation is a set of ordered pairs.
     
 
2
,
4
,
2
,
4
,
1
,
1
,
1
,
1
,
0
,
0 


A
 :
A
range
 
4
,
1
,
0
 
2
,
1
,
0
,
1
,
2 

Domain: The x values of the ordered pair.
 :
A
domain
Range: The y values of the ordered pair.
3.5 – Introduction to Functions

:
range  
6
,
5
,
4
,
3
 
3
,
2
,
1
,
4

:
domain
x y
1 3
2 5
-4 6
1 4
3 3
x y
4 2
-3 8
6 1
-1 9
5 6
x y
2 3
5 7
3 8
-2 -5
8 7
:
range  
9
,
8
,
6
,
2
,
1
 
6
,
5
,
4
,
1
,
3 

:
domain
:
range  
8
,
7
,
3
,
5

 
8
,
5
,
3
,
2
,
2

:
domain
State the domain and range of each relation.

Defn: A function is a relation where every x value has one and
only one value of y assigned to it.
x y
1 3
2 5
-4 6
1 4
3 3
x y
4 2
-3 8
6 1
-1 9
5 6
x y
2 3
5 7
3 8
-2 -5
8 7
function not a function function
State whether or not the following relations could be a
function or not.

Functions and Equations.
3
2 
 x
y
x y
0 -3
5 7
-2 -7
4 5
3 3
x y
2 4
-2 4
-4 16
3 9
-3 9
x y
1 1
1 -1
4 2
4 -2
0 0
2
x
y  2
y
x 
function function not a function
State whether or not the following equations are functions or
not.

Vertical Line Test
Graphs can be used to determine if a relation is a
function.
If a vertical line can be drawn so that it intersects a
graph of an equation more than once, then the equation
is not a function.

x
y
The Vertical Line Test
3
2 
 x
y
x y
0 -3
5 7
-2 -7
4 5
3 3
function

x
y
2
x
y 
x y
2 4
-2 4
-4 16
3 9
-3 9
function

x
y
2
y
x 
x y
1 1
1 -1
4 2
4 -2
0 0
not a function

Find the domain and
range of the function
graphed to the right.
Use interval
notation.
x
y
Domain:
Domain
Range:
Range
[–3, 4]
[–4, 2]
Domain and Range from Graphs

Find the domain
and range of the
function graphed to
the right. Use
interval notation.
x
y
Domain:
Domain
Range:
Range
(– , )
[– 2, )
Domain and Range from Graphs

Function Notation
  1
3 
 x
x
f
  1
3 
 x
x
y
   
x
f
x
y
y 

Shorthand for stating that an equation is a function.
1
3 
 x
y
Defines the independent variable (usually x) and the
dependent variable (usually y).
3.6 – Function Notation

  5
2 
 x
x
f
Function notation also defines the value of x that is to be use
to calculate the corresponding value of y.
    5
3
2
3 

f
  1
3 
f
 
1
,
3
f(x) = 4x – 1
find f(2).
f(2) = 4(2) – 1
f(2) = 8 – 1
f(2) = 7
(2, 7)
g(x) = x2
– 2x
find g(–3).
g(–3) = (-3)2
– 2(-3)
g(–3) = 9 + 6
g(–3) = 15
(–3, 15)
find f(3).

Given the graph of
the following function,
find each function
value by inspecting
the graph.
f(5) = 7
x
y
f(x)
f(4) = 3
f(5) = 1
f(6) = 6
●
●
●
●

�ݺ�ߣ

1_Relations and Functions grade eight.pptx

Recommended

More Related Content

Similar to 1_Relations and Functions grade eight.pptx (20)

More from IgopAuhsoj (7)

Recently uploaded (20)

1_Relations and Functions grade eight.pptx

Editor's Notes