How do you decide whether the relation # x^2 + y = 81# defines a function?
A function is a law of association between elements in two different sets.
So, to define a function, you must have a "starting" set
In most cases, students deal with numerical functions, i.e. functions in which both domain and codomain are the set of real numbers
So, does your equation describes a function? It depends on the variable we choose and independent:
In this case, we're looking for a rule that assigns a value to
which is indeed a function: for every value
This case is the other way around: we're looking for a rule that assigns a value to
which is not a function: for every value
Assume, for example,
So, in this case, we're not able to associate one and only one output value to our input value.