Characteristics of Rational Functions - Exit ticket

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What is a rational function?

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A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

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What is an asymptote?

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An asymptote is a line that a graph approaches but never touches or crosses.

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What is a vertical asymptote?

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A vertical asymptote occurs at values of x that make the denominator of a rational function zero, indicating where the function is undefined.

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What is a horizontal asymptote?

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A horizontal asymptote describes the behavior of a function as x approaches positive or negative infinity.

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What is a slant (oblique) asymptote?

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A slant asymptote occurs when the degree of the numerator is one greater than the degree of the denominator, and it can be found using polynomial long division.

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How do you find the y-intercept of a rational function?

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To find the y-intercept, evaluate the function at x = 0, provided the function is defined at that point.

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What is the domain of a rational function?

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The domain of a rational function includes all real numbers except those that make the denominator zero.

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What is the significance of the y-intercept?

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The y-intercept indicates the point where the graph crosses the y-axis, providing insight into the function's behavior.

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

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Vertical asymptotes can be found by setting the denominator equal to zero and solving for x.

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What is the relationship between the degrees of the numerator and denominator in determining horizontal asymptotes?

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If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If they are equal, the horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator.