Operations on Rational Functions HA2

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 any common factors.

Front

What are the restrictions on the domain of a rational function?

Back

The restrictions on the domain of a rational function are the values of the variable that make the denominator equal to zero.

Front

What does it mean to multiply rational functions?

Back

Multiplying rational functions involves multiplying the numerators together and the denominators together, then simplifying the resulting expression.

Front

How do you divide rational functions?

Back

To divide rational functions, multiply the first rational function by the reciprocal of the second rational function and simplify.

Front

What is the process for finding the least common denominator (LCD) of rational expressions?

Back

To find the least common denominator, factor each denominator and take the highest power of each factor that appears.

Front

What is the difference between proper and improper rational functions?

Back

A proper rational function has a degree of the numerator less than the degree of the denominator, while an improper rational function has a degree of the numerator greater than or equal to the degree of the denominator.

Front

What is the significance of vertical asymptotes in rational functions?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, indicating where the function approaches infinity.

Front

How do you find horizontal asymptotes of a rational function?

Back

Horizontal asymptotes are found by comparing 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, no horizontal asymptote.

Front

What is the process for adding rational functions?

Back

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