Rational Functions

Front

What is a rational function?

Back

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

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

Back

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 canceled factor.

Front

What is a point of discontinuity?

Back

A point of discontinuity is a value of x where a function is not continuous, which can occur due to holes or vertical asymptotes.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity as x approaches a, typically found where the denominator is zero.

Front

How do you determine vertical asymptotes?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

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

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, there is no horizontal asymptote.

Front

What is the range of a rational function?

Back

The range of a rational function is the set of all possible output values (y-values) that the function can produce, often determined by analyzing asymptotes and holes.

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Back

It means that the function can take any value except for y = 3.