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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.

Tags

CCSS.HSF-IF.C.7D

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What is an asymptote?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What is a slant (oblique) asymptote?

Back

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.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

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.

Front

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.

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

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.

Tags

CCSS.HSF-IF.C.7D