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

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

Back

Compare the degrees of the numerator and denominator.

Front

What happens if the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is at y = 0.

Front

What happens if the degree of the numerator is equal to the degree of the denominator?

Back

The horizontal asymptote is at y = the ratio of the leading coefficients.

Front

What happens if the degree of the numerator is greater than the degree of the denominator?

Back

There is no horizontal asymptote.

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

Set the denominator equal to zero and solve for x.

Front

What is the significance of asymptotes in graphing rational functions?

Back

Asymptotes indicate the behavior of the graph as it approaches certain values, helping to define the shape of the graph.

Front

What is the process to simplify a rational function?

Back

Factor the numerator and denominator, then cancel out any common factors.

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