(a) What is a function? What are its domain and range?
(b) What is the graph of a function?
(c) How can you tell whether a given curve is the graph of a function?
(a)
To explain: The terms function, domain of a function and range of a function.
A function f is defined as a ordered pair
The set of all such values of x is domain D for the function f and the set of all values of
(b)
To explain: The meaning of graph of the function f.
Graph:
Draw the graph of the function f as shown in the Figure1
As per the definition of the function it is an ordered pair
Plot the point
Connect all the points to obtain a curve this curve is known as graph of the function f.
(c)
To check: Whether the graph of a function exists or not.
If the graph has no vertical line intersects to the curve more than once, then the graph of a function exists.
If the graph has the vertical line intersect to the curve more than once, then the graph of a function does not exist