Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Real value functions and their graphs

A function  f: A\rightarrow B where  B \subseteq R is called a real valued function or a real function.

Thus  f: A\rightarrow B , for  x \in A , F a unique  y \in B such that  y=f(x)

 \rightarrow Domain:

Let  f: A\rightarrow B , where  A and  B are subsets of   R then \text {dom} = D_f = A = \{1,2,3\}

 \rightarrow Codomain:

Let  f: A\rightarrow B , where  A and  B are subsets of  R then codomain of f = B = \{4,8,12\}

 \rightarrow Range:

 \text {rng}f= f(A) \subseteq B

 \text {rng}f = f(A)=B, i.e., f(1)=4 , f(2)= 8 , f(3)= 12

 \rightarrow Graphs:

Let  f: A\rightarrow B , where  A\subseteq R , then G_f =\{(x,f(x)) | x \in \text{ dom } f\} is called graph of  f .

 \rightarrow The graph of  f corresponds to a set of points on the cartesian plane.

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