Any value of x that would make the denominator of a rational function zero is outside the domain. Graphically, these excluded x values can show up either are holes in the graph, which are called discontinuities. If there is a factor of the numerator that is also a factor of the denominator, then the zero of that factor is a hole on the graph. To find the y value of that hole, plug the x value into the reduced function and solve for y. A zero that comes from a factor of the denominator only is called a vertical asymptote. The x values will get infinitely close to this vertical line as the y values head to either positive or negative infinity.
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