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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.
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.
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A rational function is an equation that takes the form y = N(x)/D(x) where N and D are polynomials. Attempting to sketch an accurate graph of one by hand can be a comprehensive review of many of the most important high school math topics from basic algebra to differential calculus. [1]
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.
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.
11.1: Graphs of rational functions. Recall from the beginning of this chapter that a rational function is a fraction of polynomials: f(x) = anxn + an − 1xn − 1 + ⋯ + a1x + a0 bmxm + bm − 1xm − 1 + ⋯ + b1x + b0. In this section, we will study some characteristics of graphs of rational functions.
Determine which of four graphs fits the formula of a given function. Skip to main content If you're seeing this message, it means we're having trouble loading external resources on our website.
Graphing Rational Functions. In Example 9, we see that the numerator of a rational function reveals the x-intercepts of the graph, whereas the denominator reveals the vertical asymptotes of the graph. As with polynomials, factors of the numerator may have integer powers greater than one.