I assume you mean "relation". By definition, all functions are relations; but only some relations are functions.
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You cannot, necessarily. Given a graph of the tan function, you could not.
For example, the derivate of x2 is 2x; then, an antiderivative of 2x is x2. That is to say, you need to find a function whose derivative is the given function. The antiderivative is also known as the indifinite integral. If you can find an antiderivative for a function, it is fairly easy to find the area under the curve of the original function - i.e., the definite integral.
A function must have a value for any given domain. For each edge (or interval), the sign graph has a sign (+ or -) . So, it is a function.
A logistic function or curve is a mathematical function having an S shape, known as sigmoid curve. The name was given by Pierre Francois Verhulst in either the year of 1844 or 1845.
A derivative of a function represents that equation's slope at any given point on its graph.