Rational Functions

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.

Tags

CCSS.HSF-IF.C.7D

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity as x approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that the function approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided those values do not cancel with the numerator.

Tags

CCSS.HSF-IF.C.7D

Front

What is a hole in a rational function?

Back

A hole occurs at a value of x where both the numerator and denominator are zero, indicating a removable discontinuity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator: if the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the degree of a polynomial in a rational function?

Back

The degree of the polynomial affects the behavior of the function, including the number of asymptotes and the end behavior of the graph.

Tags

CCSS.HSF-IF.C.7D

Front

What happens to a rational function as x approaches infinity?

Back

As x approaches infinity, the function approaches its horizontal asymptote, if one exists.

Tags

CCSS.HSF-IF.C.7D

Front

What is the relationship between zeros of the numerator and vertical asymptotes?

Back

Zeros of the numerator indicate x-intercepts, while vertical asymptotes are determined by zeros of the denominator.

Tags

CCSS.HSF-IF.C.7D

Front

What is the formula for finding the horizontal asymptote when degrees are equal?

Back

If the degrees of the numerator and denominator are equal, the horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Tags

CCSS.HSF-IF.C.7D