Unwrapping The Basics Of Rational Functions: Properties, Domain, Range, And Graphing Techniques

Rational Function

f(x) = 1/x

A rational function is a function that can be expressed as the ratio of two polynomial functions. It is commonly represented as f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, and Q(x) is not equal to zero.

Rational functions can have a variety of properties, including a vertical or horizontal asymptote, holes in the graph, and vertical and horizontal shifts. The degree of the polynomials in the numerator and denominator determine the behavior of the function near these asymptotes.

One important aspect of rational functions is their domain and range. The domain of a rational function is all the values of x for which the denominator is not equal to zero. The range of a rational function is all the values of y that can be obtained from the function.

To graph a rational function, we first need to find its intercepts, asymptotes, and other important points. Then, we can use that information to sketch the graph using a table of values or a graphing calculator.

Rational functions have many important applications in fields such as physics and engineering. For example, they can be used to model the behavior of a system as a function of input and output variables.

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