Rational Functions Test Review

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 are vertical asymptotes?

Back

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

Front

What are horizontal asymptotes?

Back

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

Front

How do you find vertical asymptotes?

Back

Set the denominator of the rational function equal to zero and solve for x.

Front

How do you find horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator: If degree of numerator < degree of denominator, y=0; if equal, y= leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What is the significance of holes in rational functions?

Back

Holes occur at points where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

What does it mean to simplify a rational function?

Back

To simplify a rational function means to reduce it to its lowest terms by canceling common factors in the numerator and denominator.

Front

What is the transformation of the function f(x) = (x+6)/(x-5) when it is shifted left 3 units?

Back

The transformed function is f(x) = (x+3)/(x-5).

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator equals zero.

Front

What is the range of a rational function?

Back

The range of a rational function is all real numbers except for the horizontal asymptote.