Rational Graphs

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

What is a vertical asymptote?

Back

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

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

What is a horizontal asymptote?

Back

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

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes can be found 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.

Front

What is the range of a rational function?

Back

The range of a rational function includes all real numbers except for values that the function cannot take, often determined by horizontal asymptotes.

Front

What is the significance of holes in a rational function?

Back

Holes occur in a rational function when a factor cancels out in both the numerator and denominator, indicating a point where the function is undefined.

Front

What is the end behavior of a rational function?

Back

The end behavior describes how the function behaves as x approaches positive or negative infinity, often determined by the leading coefficients and degrees.