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 find vertical asymptotes of a rational function?

Back

Vertical asymptotes are found by setting the denominator equal to zero and solving for x.

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 does it mean if a factor in the denominator cancels out?

Back

If a factor in the denominator cancels out with a factor in the numerator, it indicates a hole in the graph, not a vertical asymptote.

Front

What is the domain of a rational function?

Back

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

Front

How do you find the x-intercepts of a rational function?

Back

To find the x-intercepts, set the numerator equal to zero and solve for x.

Front

What is the significance of the degrees of the numerator and denominator?

Back

The degrees of the numerator and denominator help determine the behavior of the function at infinity and the presence of horizontal asymptotes.

Front

What is a hole in a rational function?

Back

A hole occurs at a value of x where a factor cancels out, indicating that the function is not defined at that point.

Front

How do you find the y-intercept of a rational function?

Back

To find the y-intercept, evaluate the function at x = 0.

Front

What is the relationship between the leading coefficients and horizontal asymptotes?

Back

If the degrees of the numerator and denominator are equal, the horizontal asymptote is the ratio of the leading coefficients.