Rational Functions End Behavior/Discontinuity Flashcard

Front

What is a rational function?

Back

Front

What is the end behavior of a rational function?

Back

The end behavior of a rational function describes how the function behaves as x approaches positive or negative infinity. It is determined by the degrees of the numerator and denominator.

Front

How do you determine the x-intercept of a rational function?

Back

To find the x-intercept, set the numerator equal to zero and solve for x. The x-intercept occurs where the function crosses the x-axis.

Front

What happens to the end behavior of a rational function when the degree of the numerator is less than the degree of the denominator?

Back

The end behavior approaches zero as x approaches positive or negative infinity.

Front

What is a vertical asymptote in a rational function?

Back

A vertical asymptote occurs at values of x that make the denominator equal to zero, indicating that the function approaches infinity or negative infinity.

Front

What is a horizontal asymptote in a rational function?

Back

A horizontal asymptote describes the behavior of a rational function as x approaches infinity. It can be determined by comparing the degrees of the numerator and denominator.

Front

What is the significance of the degrees of the numerator and denominator in determining end behavior?

Back

The degree of the numerator and denominator helps determine the end behavior: if degrees are equal, the horizontal asymptote is the ratio of leading coefficients; if the numerator's degree is less, the horizontal asymptote is y=0; if greater, there is no horizontal asymptote.

Front

What is a hole in a rational function?

Back

A hole occurs at a value of x that makes both the numerator and denominator equal to zero, indicating a point of discontinuity in the graph.

Front

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

Back

To find the y-intercept, substitute x=0 into the function and solve for y.

Front

What is the relationship between the x-intercept and the roots of the numerator?

Back

The x-intercepts of a rational function correspond to the roots of the numerator, where the function equals zero.