Rational and Variation Practice

Front

What is a rational function?

Back

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

How many vertical asymptotes can a rational function have?

Back

A rational function can have one or more vertical asymptotes, depending on the values of x that make the denominator zero.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote describes the behavior of the function as x approaches infinity or negative infinity.

Front

What is the domain of a rational function?

Back

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

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 the significance of the degree of the numerator and denominator in determining horizontal asymptotes?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. If they are equal, the asymptote is y=\frac{a}{b}, where a and b are the leading coefficients.

Front

What is a slant (oblique) asymptote?

Back

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

Front

What does it mean if a function has no horizontal asymptote?

Back

If a function has no horizontal asymptote, it means that as x approaches infinity or negative infinity, the function does not approach a constant value.

Front

What is the range of a rational function?

Back

The range of a rational function is the set of all possible output values, which can be affected by vertical asymptotes and holes in the graph.