14075517 chapter 3_-_relation_and_function

BBMP 1103
Management Mathematics
Chapter:3 – Introduction to
Functions

Prepared by

Richard Ng

BBMP1103 – Chapter 3 - Richard Ng (2008) Page 1 of 25

1. Relations and Functions
Four types of relations:

X Y X Y

One to One One to Many

X Y X Y

Many to One Many to Many


Prepared by: Richard Ng (OUM Perak) 1

2. Function
Any relations that produce only one output:

X Y

One to One

X Y

Many to One


Example: 1
Which of the following equations will define y as a
function of x?
y
y = 3x
a) y = 3 x

x

The above relation is a 1 to 1 (Answer: Function)



b) y = x2
y

y = x2

x

The above relation is a Many to 1 (Answer: Function)


c) y=± x atau y2 = x

y

y2 = x

x

The above relation is a 1 to Many (Answer: Not Function)



d) y = 6

y

y=6

x

The above relation is a Many to 1 (Answer: Function)


e) x = 5

x=5
y

x

The above relation is a 1 to Many (Answer: Not Function)



Exercise: 3.2
Which of the following graphs represent a function of x?
y y
a) b)

0 x

0 x

The above relation is a One The above relation is a One
to One. to Many.
Answer: Function Answer: Not Function


y y
c) d)

0 x 0 x

to One. to One.
Answer: Function Answer: Function



y
e) f) y

0 x

0 x

to One. to Many.
Answer: Function Answer: Not Function


3. Function, Domain and Range

Domain = is a set of all values of x that defines y
Range = is a set of all values of y for a given domain
Example: 2
Determine the domain and range of the following functions:
a) y = 3 x
y = 3x
y
y →∝
Domain = all values of x
where x ∈ R

∝← x
x →∝
x

Range = all values of y
where y ∈ R
y →∝


b) y = x2
y →∝
y

y = x2

∝← x y=0 x →∝
x

Domain = all values of x Range = all values of y
where x ∈ R where y ∈ R and y ≥ 0


1
c) y = y
x 1
y=
y →∝ x

∝← x x≠0
x≠0 x →∝ x

y →∝

Domain = all values of x where Range = all values of y where
x ∈ R and x ≠ 0 y ∈ R and y≠0



d) y = x + 3 atau y = x + 3
2

y
y →∝
y2 = x + 3

x = −3 x
x →∝

y →∝

x ∈ R and x ≥ −3 y∈R


Exercise 3.3:
Determine the domain and range of the following functions:

a) f(x) = 2x y
y = 2x
y →∝

∝← x
x
x →∝

y →∝

x∈R y∈R



b) f(x) = 3 - x
y →∝
y

y = 3− x

x →∝

∝← x
x

y →∝

x∈R y∈R


c) f(x) = x2 + 1
y

y →∝
y = x2 + 1

y =1

∝← x
x
x →∝

x∈R y ∈ R and y ≥ 1



1
d) f(x) =
x−4
1
y= x−4 ≠ 0
x−4

Domain = all values ≠ 4 where
x of x x ∈ R and x ≠ 4

Denominator
1 1 cannot be zero
x−4= x= +4
y y

of where y ∈ R and
Range = all valuesx ≠y4 y≠0
y≠0


e) f(x) = x

y= x x≥0

Domain = all values ≠ 4 where
x of x x ∈ R and x ≥ 0

x = y2 y →∝

Range = all values of y where y ∈ R
x≠4
y≠0



Exercise 3.4:
a) y

y →∝

x →∝
∝← x
x

y →∝

x∈R y∈R


b) y

y=n

∝← x
x
x →∝

y →∝

x∈R y ∈ R and y ≤ n



c) y

y →∝

∝← x y>0 x →∝ x

x∈R y ∈ R and y > 0


y
d)
y →∝

y>0
x≠0 x
∝← x x →∝

x ∈ R and x ≠ 0 y ∈ R and y > 0



End of
Chapter
3



14075517 chapter 3_-_relation_and_function

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