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In this lesson, you will learn what a rational function is in Algebra. Specifically, we will discuss how to graph a rational function by first finding the domain of the function.
The domain of the rational function are any points that cause a vertical asymptote to appear on the graph – those are the points that cause the function to approach infinity. Setting the denominator equal to zero yields the points that are excluded from the domain and are the same points where the vertical asymptotes lie.
If we set the numerator of the rational function equal to zero and solve, we will find the points that cause the function to approach zero. In other words, these are the points where the function crosses the x-axis.
Finding the domain and the zeros of a rational function is the first step necessary to sketch a graph of it on the x-y plane.