rational functions graphs

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What is a rational function?

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What is a hole in a rational function graph?

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A hole in a rational function graph occurs at a value of x where both the numerator and denominator of the function equal zero, indicating that the function is undefined at that point.

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

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The vertical asymptote of a rational function occurs at the values of x that make the denominator equal to zero, provided that these values do not also make the numerator zero.

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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 x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values.

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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 leading coefficient in a rational function?

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The leading coefficient of the polynomial in the numerator or denominator affects the end behavior of the rational function, particularly in determining the horizontal asymptote.

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What does it mean if a rational function has a hole at x = -3?

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If a rational function has a hole at x = -3, it means that the function is undefined at this point, and the graph will not include the point ( -3, f(-3) ).

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How can you identify a hole in a rational function from its equation?

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To identify a hole in a rational function, factor both the numerator and denominator. If a common factor exists, the x-value that makes this factor zero indicates the location of the hole.

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

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A hole indicates a point where the function is undefined due to a common factor in the numerator and denominator, while a vertical asymptote indicates a value where the function approaches infinity.

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What is the general form of a rational function?

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