Graphing 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

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.

Front

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

Back

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

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

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator Q(x) equal to zero, provided these values do not also make the numerator zero.

Front

What is a hole in a rational function?

Back

A hole occurs at a value of x where both the numerator and denominator are zero, indicating a removable discontinuity.

Front

How do you identify holes in a rational function?

Back

To identify holes, factor both the numerator and denominator, and find common factors that cancel out.

Front

What is a horizontal asymptote?

Back

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

Front

How do you determine horizontal asymptotes for rational functions?

Back

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

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is one greater than the degree of the denominator.