Rational functions Flashcard

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 the horizontal asymptote of a rational function?

Back

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

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Back

If n < m, the horizontal asymptote is y = 0. If n = m, the horizontal asymptote is y = \frac{a}{b}. If n > m, there is no horizontal asymptote.

Front

What does it mean if a rational function has a vertical asymptote?

Back

A vertical asymptote occurs where the function approaches infinity or negative infinity, typically at values of x that make the denominator zero.

Front

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

Back

Set the denominator equal to zero and solve for x.

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What is the significance of the x-intercepts in a rational function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by setting the numerator equal to zero.

Front

What is the significance of the y-intercept in a rational function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

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x = 5, x = 3

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x = -6, x = 4

Front

What transformation occurs when a function is translated right and down?

Back

The graph of the function shifts to the right by a certain number of units and down by a certain number of units.