Math 3 Fall Final Review

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What is a hole in a function?

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A hole occurs in a function at a point where the function is not defined due to a factor that cancels out in the numerator and denominator.

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What does the term 'domain' refer to in a function?

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The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What are the zeros of a function?

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Zeros of a function are the values of x for which the function equals zero. They are found by setting the function equal to zero and solving for x.

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What is multiplicity in relation to zeros?

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Multiplicity refers to the number of times a particular zero occurs. A zero with multiplicity greater than 1 indicates that the graph touches the x-axis at that point.

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How do you find the vertical asymptotes of a rational function?

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Vertical asymptotes occur at values of x that make the denominator zero, provided those values do not also make the numerator zero.

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What is the difference between a hole and a vertical asymptote?

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A hole occurs when a factor cancels out in both the numerator and denominator, while a vertical asymptote occurs where the denominator is zero but the numerator is not.