Subject: Maths, asked on 4/5/18

## Explain Signum function Subject: Maths, asked on 4/5/18

## Q. What is Rational function?

Subject: Maths, asked on 4/5/18

## Explain Modulus function

Subject: Maths, asked on 4/5/18

## Example .13. Define the function f : $R\to R$ by y = f (x), x $\in$ R. Complete the table given below by using this definition. What is the domain and range of the function? Draw the graph of f.

Subject: Maths, asked on 4/5/18

## Polynomial function

Subject: Maths, asked on 4/5/18

## Q.(ii). Constant function: Define the function by y = f (x) = c, x $\in$ R where c is a constant and each x $\in$ R. Here domain of f is R and its range is {c}.

Subject: Maths, asked on 4/5/18

## Explain Identity functions

Subject: Maths, asked on 4/5/18

## Example 12 Let N be a set of natural numbers. Define a real valued function. x 1 2 3 4 5 6 7 y f(1) =  ...... f(2) =  ...... f(3) =  ...... f(4) =  ...... f(5) =  ...... f(6) =  ...... f(7) =  ......

Subject: Maths, asked on 4/5/18

## Definition 6: Definition 6 A function which has either R or one of its subsets as its range is called a real valued function. Further, if its domain is also either R or a subset of R, it is called a real function.

Subject: Maths, asked on 4/5/18

## Explain functions and definition 5: A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B.

Subject: Maths, asked on 4/5/18

## Explain Remarks A relation R from A to A is also stated as a relation on A.

Subject: Maths, asked on 4/5/18

## Q). Explain note Note: The total number of relations that can be defined from a set A to a set B is the number of possible subsets of $A×B$. If n(A) = p and n(B) = q, then $n\left(A×B\right)=pq$ and the total number of relations is ${2}^{pq}$.

Subject: Maths, asked on 4/5/18

## Example 7: Example 7:-  Let A=, {1,2,3,4,5,6}. Define a relation R from A to A by R={(x,y):y=x+1} (i) Depict this relation using an arrow diagram. (ii) Write down the domain, codomain the range of R.

Subject: Maths, asked on 4/5/18

## Explain Remarks Remarks   (i) A relation may be represented algebraically either by the Roster method or by the Set-builder method.  (i)  An arrow diagram is a visual representation of a relation.

Subject: Maths, asked on 4/5/18

## Meaning of definition 2,3,4 Definition 2 A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product AxB. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A X B. The second element is called the image of the first element.  Definition 3 The set of all first elements of the ordered pairs in a relation R from a set A to set B is called the domain of the relation R.  Definition 4 The set of all second elements in a relation R from a set A to a set B is called the range of the relation R. The whole set B is called the codomain of the relation R. Note that range $\subseteq$ codomain.

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