4-2 Graphing Rational Functions

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What is a horizontal asymptote?

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A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity.

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What are vertical asymptotes?

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Vertical asymptotes are vertical lines that the graph of a function approaches as the input (x) approaches a certain value, typically where the function is undefined.

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The vertical asymptotes are at x = 0 and x = -2.

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What is an asymptote?

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An asymptote is an imaginary line that a graph approaches but never touches.

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How do you determine the horizontal asymptote of a rational function?

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What is the significance of the degree of a polynomial in determining asymptotes?

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The degree of the polynomial in the numerator and denominator helps determine the existence and location of horizontal and vertical asymptotes.

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There is no horizontal asymptote since the degree of the numerator (3) is greater than the degree of the denominator (2).

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What happens to the graph of a rational function near its vertical asymptotes?

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The graph will approach the vertical asymptote but will never cross it, often going to positive or negative infinity.