It can be determined that a relation represented as an equation is a function if and only if for each value on x-axis, there is a corresponding value on Y-axis.
which also signifies that for each value of x , there is a value of y which exists and is real.
A function is a mapping from one set to another such that nothing in the first set is mapped to more than one thing in the second set.
Or in simple words if there is no corresponding value of y for any x, then that is not a function.
For example,
[tex]x^{2} +y^{2}[/tex]=1
when the value of x is 0 , then value of y is 1 or -1, Thus, it will not be a function.
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