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

What is

1. Introduction to Function:

Function = a rule that assigns each input number (x)

exactly one output number (y)

Function :UniversityInput: Students

Output: Graduate/

Worker

Mohd noor abdul hamid : [email protected]

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 2Mohd noor abdul hamid : [email protected]

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

2If f(x) = 6, determine the corresponding value of x

Solution:

f(x) = 6 = x2+3

2

12 = x2+3

9 = x2

x = ±3Mohd noor abdul hamid : [email protected]

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 }

InputOutput

Function


F(x) = fry

Output

Input

Domain = { everything that can be fry}

Range =

{all frie

d fo

od}


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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