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OUR PRESENTATION

Topic of our presentation: Function

Submitted forMd. Shahjalal Talukdar

Submitted ByMd. Abu RayhanID: 161-15-7189

Sabbir Ahmed AkkharID: 161-15-7534Md. Anik Khan

ID: 161-15-Alif Bin Rahman Khan

ID:161-15-Kaniz Assami

ID: 161-15-7608

What is Function?

Ans: A function is a rule which relates the values of one variable quantity to the values of another variable quantity, and does so in such a way that the value of the second variable quantity is uniquely

determined by the value of the first variable quantity.

Functions vs. Relations A "relation" is just a relationship between sets of

information.

A “function” is a well-behaved relation, that is, given a starting point we know exactly where to go.

What are the domain and range of a function?

The domain is the set of all the values of the independent variable, the x-coordinate.

The range is the set of all the values of the dependent variable, the y-coordinate.

Identify the domain and range of the function below.

{ 2, 7), (4, 11), (6, 15), (8, 19)}

The domain is { 2, 4, 6, 8}

The range is { 7, 11, 15, 19}

NB: All input = Domain & All outputs = Range

Graphs

The domain of a function is the set of all the x-coordinates in the functions’ graph

Domain 3 ≤ x ≤ 12

The range of a function is the set of all the y-coordinates in the functions’ graph

Range 6 ≤ y ≤ 12

A One to One function

A function is one to one if no more than one element in the domain is paired with an element in the range.

Examples of one to one functions

Note every Uppercase number has exactly one lower case partner

A

B

C

A

B

C

a

b

c

1. f (x) = 3x +5 2. 3. All odd functions

3)( xxf

Onto Function

In mathematics, a function f from a set X to a set Y is subjective (or onto), or a surjection, if every

element y in Y has a corresponding element x in X such that f(x) = y. The function f may map more than one element of X to the same element of Y.

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