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 to identify when graphing a rational function?

Back

Key features include intercepts, asymptotes (vertical and horizontal), and the behavior of the function as it approaches these asymptotes.

Front

How do you find the vertical asymptotes of a rational function?

Back

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

Front

What is a horizontal asymptote and how is it determined?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity. It is determined by comparing the degrees of the numerator and denominator.

Front

What is the difference between a hole and a vertical asymptote in a rational function?

Back

A hole occurs when a factor in the numerator and denominator cancels out, while a vertical asymptote occurs where the denominator is zero and the numerator is not.

Front

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

Back

The x-intercepts are found by setting the numerator equal to zero and solving for x.

Front

What is the significance of the degree of the numerator and denominator in a rational function?

Back

The degree of the numerator and denominator helps determine the end behavior of the function and the presence of horizontal asymptotes.

Front

What is the process for graphing a rational function?

Back

1. Identify intercepts and asymptotes. 2. Determine the behavior near the asymptotes. 3. Plot additional points to understand the shape of the graph.

Front

What role do intercepts play in graphing rational functions?

Back

Intercepts provide key points on the graph where the function crosses the axes, helping to shape the overall graph.

Front

How can you determine the end behavior of a rational function?

Back

End behavior can be determined by analyzing the leading coefficients and degrees of the numerator and denominator.