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In this section we will use the zeros and asymptotes of the rational function to help draw the graph of a rational function. We will also investigate the end-behavior of rational functions. Let’s begin with an example.
This section covers the graphing of rational functions, focusing on identifying key features such as vertical and horizontal asymptotes, intercepts, and end behavior. It explains how to analyze the …
How To: Given a rational function, sketch a graph. Evaluate the function at 0 to find the y-intercept. Factor the numerator and denominator. For factors in the numerator not common to the denominator, determine where each factor of the numerator is zero to find the [latex]x[/latex]-intercepts.
To obtain a better idea of some of these features including asymptotes, we start by graphing some rational functions. In particular it is useful to know the graphs of the basic functions \(y=\dfrac 1 {x^n}\).
In this section we will discuss a process for graphing rational functions. We will also introduce the ideas of vertical and horizontal asymptotes as well as how to determine if the graph of a rational function will have them.
Learning Objectives. Graph the rational function f (x)= 1/x f ( x) = 1 / x. Describe the features of the rational function f (x) =1/x f ( x) = 1 / x. Asymptotes. Symmetry. Domain and Range. The most basic rational function is f (x) = 1 x f ( x) = 1 x.
Characteristics of Rational Functions. We have seen the graphs of the basic reciprocal function and the squared reciprocal function from our study of toolkit functions. Examine these graphs and notice some of their features. Several things are apparent if we examine the graph of f\left (x\right)=\frac {1} {x} f (x) = x1.
How To: Given a graph of a rational function, write the function. Determine the factors of the numerator. Examine the behavior of the graph at the x -intercepts to determine the zeroes and their multiplicities.
A rational function is a fraction of polynomials. Asymptotes play an important role in graphing rational functions. Learn how to find the domain and range of rational function and graphing it along with examples.