Characteristics of Rational Functions - Exit ticket

Front

What is a rational function?

Back

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?

Back

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

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What is a horizontal asymptote?

Back

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

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

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To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, divide the leading coefficients.

Front

What is a vertical asymptote?

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A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value, typically where the function is undefined.

Front

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

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To find the vertical asymptote, set the denominator equal to zero and solve for x.

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What is a hole in a rational function?

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A hole occurs in a rational function at a value of x that makes both the numerator and denominator zero, indicating a removable discontinuity.

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How do you find the coordinates of a hole in a rational function?

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To find the coordinates of a hole, factor the numerator and denominator, cancel the common factors, and evaluate the function at the x-value of the hole.

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What are the coordinates of the y-intercept of a rational function?

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The coordinates of the y-intercept are found by evaluating the function at x=0, provided the function is defined at that point.

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What does it mean if a rational function has no y-intercept?

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If a rational function has no y-intercept, it means that the function is undefined at x=0.