In this lesson, we learn how to determine the locations of holes in the graph of a rational function which has common factors in both the numerator and denominator. If both the numerator and the denominator have the same factor, x minus b, then there is a hole in the graph at the point where x equals b, unless the line x equals b is a vertical asymptote. We see this process in action by taking an example of f of x equals x squared plus x minus 6 over x minus 2, factoring it out, canceling common factors, and plotting the hole on the graph.
Given a rational function which has common factors in both the numerator and denominator, determine the locations in the graph of the simplified expression where holes would be located.
Questions answered by this video:
What are holes in the graphs of rational functions?
When is a rational function undefined?
Where is f(x) = (x^2 + x - 6)/(x - 2) undefined?
How can you identify holes in the graph of a function?
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This lesson explains the concept of holes in graphs of rational functions where the function is undefined. The graph of this function appears to be a straight line except there is a hole in one spot on the graph.