Introduction to Function, Domain and Range - Mohd Noor

I N T R O D U C T I O N T O
Mohd Noor Abdul Hamid, Ph.D

1. Introduction to Function:
Function = a rule that assigns each input number (x)
exactly one output number (y)
Function :UniversityInput: Students
Output: Graduate/
Worker
Mohdnoorabdulhamid : mohdnoor@uum.edu.my

y = x + 2
Function fx = 1
Input (x)
1 + 2 = 3
Output (y)
x = -4 -4 + 2 = -2
Thus, the rule define y as a function of x
1 to 1

y2 = xX = 9
Y = + 3
Y = - 3
y2 = x did not define y as a function of x
1 to Many

Y = x2 -1
X = 3
Y = 8
X = -3
Y = x2-1 did / did not define y as a function of x??
Many to 1

2. Functional Notation
Usually, the letters ƒ, g, h, F, G is used to
represent the function rules.
Example: y = x + 2 can be written as,
ƒ(x) = x + 2, where ƒ(x) is the output
for the function ƒ
with x as the input
Therefore, the output ƒ(x) is equal to y
(that is : y = ƒ(x))

Example : Given the function f(x) = 4x – 3
5
a)Compute f(2)
f(2) = 4(2) – 3 = 5 = 1
5 5
b) What is the value of x, if f(x) = 3?
3 = 4x – 3
5
15 = 4x -3
18 = 4x
x = 18 = 9
4 2

Exercise 1:
Find the value f(3) for the function
f(x)=2x-1
Solution:
f(3) = 2(3) -1
= 6 -1
= 5

Exercise 2:
Given the function:
f(x) = x2 + 3
2
If f(x) = 6, determine the corresponding value of x
Solution:
f(x) = 6 = x2+3
2
12 = x2+3
9 = x2
x = ±3

Exercise 3:
Given h(u) =
u
u 4
Find:
a)h(5)
b)h(-4)
c)h(u-4)
Answer:
a)±3/5
b) 0
c) u
u-4

Exercise 4:
Given f(x) = 4,
Find f(4), f(1/100) and f(x+4)
Answer: 4
1/100 4 10
f(x)
x
4

3. Domain and Range
Domain : set consist of all valid input (x)
for a given function
Range : set consist of all valid output (y)
for a given function
(produce by the values in the
domain)

Domain?? { Egg , Rice , Chicken ………..}
{everything that can be fry}
Range?? { Fried Egg, Fried Rice, Fried Chicken…….}
{ all fried food }
Input
Output
Function

F(x) = fry
Output
Input
Domain = { everything that can be fry}
Range={allfriedfood}

Example:
Given the function :
y=f(x) = 2x
5
0
-7
+
:
:
:
:
:
:
-
10
0
-14
+
:
:
:
:
:
:
-
Domain
{x ε R}
Range
{y ε R}

F(x)/y
x
Y = 2x
2 4-2
4
8
-4
Domain = ??
Range = ??
Example 2:
{ any real numbers (R)} or can be written as
{ y Є R}
+
{any real numbers (R)} or can be written as
{ x Є R}
- +

What have you learnt today??
• Definition of function
- determine whether a mathematical
statement is a function or not.
- determine the input/output of a
function
• Concept of Domain and function
- determine the domain and range of a
given function

Example 3:
Y = 2x +2
2 4
6
10
Domain ??
Range??
{ 2 ≤ x ≤ 4 }
Domain
{ 6 ≤ y ≤ 10 }
Range
x
y

Example 4 :
3
10
5
26
Domain = { 3 ≤ x < 5 }
Range = { 10 ≤ y < 26 }
y
x

-1
1
3
Example 5:
Domain = {x ≤ -1}
Range = { y = 1, y > 3 }
y
x

Example 6 :
1 2 3
2
4
6
0
Domain = { 0 ≤ x < 3}
Range = { y = 2, y=4, y=6}
x
y

84
2
4
Example 7:
Domain = { x > 4}
Range = {2 < y ≤ 4 }
x
y

4. Types of Function & Its Domain and Range
Form Graph Using Algebra
1. Constant Function
2. Linear Function
3. Quadratic Function
4. Polynomial/Cubic Function
5. Composite Function
6. Absolute Function
7. Rational Function
8. Square Root Function

Introduction to Function, Domain and Range - Mohd Noor

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