Rational Functions Flashcard

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

How do you simplify a rational function?

Back

To simplify a rational function, factor both the numerator and the denominator and then cancel out any common factors.

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 does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

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

Back

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

Front

What is a horizontal asymptote?

Back

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

Front

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

Back

A removable discontinuity occurs when a factor cancels out in a rational function, while a non-removable discontinuity occurs when the function is undefined at a certain point.

Front

How do you determine the end behavior of a rational function?

Back

The end behavior of a rational function can be determined by the degrees of the numerator and denominator polynomials.

Front

What is the significance of the leading coefficients in rational functions?

Back

The leading coefficients of the numerator and denominator determine the horizontal asymptote of the rational function.

Front

How do you perform polynomial long division?

Back

Polynomial long division involves dividing the leading term of the numerator by the leading term of the denominator and then subtracting the result from the numerator.