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Introduction to Rational Functions - Problem 8
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Dividing by zero in math is undefined, so if there is an x in the bottom of a fraction, you can expect a domain restriction, or "excluded value." These values show up as vertical asymptotes, or boundary lines, in the graph. You'll study asymptotes much more deeply in calculus, but for now, you can think of them like fences or boundaries that your graph branches can not touch. The "parent" graph of y = 1/x, including its vertical asymptotes, get shifted side to side if you introduce a number added or subtracted to x in the denominator. The graph will shift in the counter-intuitive direction: that is, it moves left if there is x + b, and moves right if there is x - b in the denominator.

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