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

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 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

What is the significance of canceling in rational functions?

Back

Canceling common factors in rational functions simplifies the expression and can help in finding limits or solving equations.

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

How do you find vertical asymptotes in rational functions?

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 infinity or negative infinity.

Front

What is the process of simplifying 15x^2/5x^3?

Back

Factor out common terms: 15x^2/5x^3 = (15/5)(x^2/x^3) = 3/x.

Front

What is the result of simplifying (x-9)/(x+9)?

Back

The simplified form is (x-9)/(x+9) as it cannot be simplified further.

Front

What is the result of simplifying 1/(3x)?

Back

1/(3x) is already in its simplest form.