Graphing a Rational Expression - Problem 5
The zeros of the denominator of a rational function are what we call points of discontinuity, or domain restrictions, and they are very important as you move toward calculus. If there is a factor of the numerator that is also a factor of the denominator, then that x value represents a hole in the graph. You can find the y coordinate of the hole by substituting the x into the reduced function. A factor that is only in the denominator represents a vertical asymptote. We talk about asymptotes in terms of what happens to the y values, or outputs, as the x values get closer and closer to those restricted values from both sides. This is a concept that you'll continue to explore in the years of math study to come.
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