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

What is the domain of a rational function?

Back

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

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided that the numerator is not also zero at those points.

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

How do you determine the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare 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 y-intercept of a function?

Back

The y-intercept of a function is the point where the graph intersects the y-axis, found by evaluating the function at x=0.

Front

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

Back

To find the y-intercept of a rational function, substitute x=0 into the function and simplify.

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient affects the end behavior of the function and helps determine the horizontal asymptote.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity occurs when a factor cancels in the numerator and denominator, while a non-removable discontinuity occurs where the denominator is zero and the numerator is not.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator equals zero, as division by zero is not possible.