Intro to 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 are the key features of a rational function's graph?

Back

Key features include intercepts, asymptotes (vertical and horizontal), and the overall shape of the graph.

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 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 are determined by comparing the degrees of the numerator and denominator polynomials.

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

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 determined by analyzing the function's behavior.

Front

What is the significance of intercepts in graphing rational functions?

Back

Intercepts (x-intercepts and y-intercepts) indicate where the graph crosses the axes and help in sketching the graph.

Front

What is a slant asymptote?

Back

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