Question

How do you know if a function is a function or not ?

Answer 1

To determine a function is a function or not ,check whether every input of x correspond to different value of y or not ,If yes then it is a function and if not it is not a function

Complete step by step solution:
To Determine whether a function is a function or not ,there are many ways to find this but before that we must know first what a function is :

So, A function is basically a relation that results in a different output for each and every different input .

For example $y = x + 7$ is function because for different values for x we put it results into different values of y or vice versa.

The best and easy way to find whether a given function is function or not is Vertical Line
Test.

Vertical Line Test: Draw graph of the relation function you wish to find then draw a vertical line that crosses the graph of the relation function .If the vertical lines crosses the graph of function only at one time then the given function is a function and if it passes the graph more than one time then the given function is not a function .

Alternative:
We can alternatively use an Input -Output Chart which shows the results of for different values of input and if one input has more than 1 no of results then the relation is not an function and if every input has different results on chart then the relation is an function

Note:
1. Important Point : Suppose different values of x as input results in the same answer then still there is a possibility that the relation given is a function .

2. To confirm your answer ,always use alternative methods also.