Introduction to Rational Function Graphs

Front

What is a rational function?

Back

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

Front

What are the characteristics of the graph of a rational function?

Back

The graph of a rational function can have vertical and horizontal asymptotes, holes, and may cross the x-axis and y-axis at certain points.

Front

What is a vertical asymptote?

Back

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

Front

What is a horizontal asymptote?

Back

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

Front

How do you find vertical asymptotes?

Back

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

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes can be determined by comparing the degrees of the numerator and denominator polynomials.

Front

What is a hole in the graph of a rational function?

Back

A hole occurs in the graph of a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

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.

Front

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

Back

The degree of the numerator and denominator helps determine the behavior of the function at infinity and the presence of horizontal asymptotes.

Front

What is the general form of a rational function?

Back

The general form of a rational function is f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials.