Rational Functions WUP-1

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, i.e., f(x) = P(x)/Q(x), where P and Q are polynomials.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function f(x) approaches infinity or negative infinity as x approaches a.

Front

What is a hole in a rational function?

Back

A hole occurs at a point x = a where both the numerator and denominator of the rational function are zero, indicating that the function is not defined at that point.

Front

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

Back

To find the x-intercept, set the numerator of the rational function equal to zero and solve for x.

Front

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

Back

To find the y-intercept, evaluate the function at x = 0, i.e., find f(0).

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the function approaches as x approaches infinity or negative infinity.

Front

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

Back

Compare the degrees of the numerator and denominator: If degree of numerator < degree of denominator, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What does the limit notation \( \lim_{x \to a} f(x) \) represent?

Back

It represents the value that f(x) approaches as x approaches a.

Front

What is the significance of \( \lim_{x \to a^-} f(x) \)?

Back

It indicates the limit of f(x) as x approaches a from the left side.

Front

What is the significance of \( \lim_{x \to a^+} f(x) \)?

Back

It indicates the limit of f(x) as x approaches a from the right side.