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 cancel out any common factors.

Front

What is the result of multiplying two negative numbers?

Back

The result of multiplying two negative numbers is positive.

Front

What is the significance of the denominator in a rational function?

Back

The denominator cannot be zero, as this would make the function undefined.

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 equal to zero.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote is determined by the degrees of the numerator and denominator polynomials.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials.

Front

How do you determine if a rational function is defined at a certain point?

Back

A rational function is defined at a point if the denominator is not zero at that point.

Front

What is the process for adding rational functions?

Back

To add rational functions, find a common denominator, rewrite each function with that denominator, and then combine the numerators.

Front

What is the process for subtracting rational functions?

Back

To subtract rational functions, find a common denominator, rewrite each function with that denominator, and then subtract the numerators.