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Is every permutation always a one-to-one function?
By definition, a permutation is a bijection from a set to itself. Since a permutation is bijective, it is one-to-one.
How do you identify the range of a function in math?
It can be quite hard. First determine the domain. Then, for every input value from the domain, calculate the output value. The set of all these output values is the range. For simple functions you will not need to find every output value. For monotonic continuous functions the end points of the domain will determine the endpoints of the range. [Monotonic means never decreasing or never increasing]. For non-monotonic functions, for example a quadratic or polynomial of higher order, you may need to find the turning points.
Is the relation a function?
Not every relation is a function. But every function is a relation. Function is just a part of relation.
How does the exponential function differ from other functions?
Every function differs from every other function. Otherwise they would not be different functions!
Why is every function a relation?
That is part of the definition of a function.
