An equation, f, has a domain of all whole numbers and has a range of all real numbers. Does the equation represent a function?
To determine whether the equation represents a function, we need to consider the definition of a function.
A function is a relation between a set of inputs (the domain) and a set of outputs (the range) such that each input is associated with exactly one output. In other words, for each input, there can be at most one output.
In this case, the equation has a domain of all whole numbers and a range of all real numbers. Since there is no restriction on the outputs, it means that for any given input, there can be multiple corresponding outputs. Therefore, the equation does not represent a function.
To see this more clearly, let's consider an example. If the equation is f(x) = x^2, the domain is all whole numbers, and the range is all non-negative real numbers. For any positive whole number input, there are two possible outputs (e.g., f(2) = 4 and f(-2) = 4). Hence, this equation does not satisfy the requirement of each input having a unique output.
In summary, if an equation has a domain of all whole numbers and a range of all real numbers, it does not represent a function.
f is not an equation.
f is a relation. Is it a function?
It cannot be a function, because more than one value of f belongs to the same value of x.
(why?)