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A formula or graph are two ways to describe a math function. How a math function is described depends on the domain of the function or the complexity of the function.
A quadratic function will have a degree of two.
A rational function is the quotient of two polynomial functions.
An alternating function is a function in which the interchange of two independent variables changes the sign of the dependent variable.
No. If the range of the first function is not the domain of the second function then the composite function is not defined.