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.

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a value of x 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 that caused the hole.

Front

What are vertical asymptotes?

Back

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

Front

How do you determine vertical asymptotes in a rational function?

Back

Vertical asymptotes can be found by setting the denominator equal to zero and solving for x, provided that the numerator is not also zero at those points.

Front

What are horizontal asymptotes?

Back

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

Front

How do you find horizontal asymptotes in rational functions?

Back

Horizontal asymptotes can be determined by comparing the degrees of the numerator and denominator polynomials.

Front

What is the significance of the range of a rational function?

Back

The range of a rational function indicates all possible output values (y-values) that the function can produce.

Front

How do you find the range of a rational function?

Back

To find the range, analyze the behavior of the function, including asymptotes and holes, and determine the values that y can take.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity occurs at a hole, while a non-removable discontinuity occurs at a vertical asymptote.