Graphs of rational functions

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical (x = a) or horizontal (y = b).

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

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

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, y = 0. If they are equal, y = leading coefficient of numerator / leading coefficient of denominator. If the numerator's degree is greater, there is no horizontal asymptote.

Front

What is a hole in a graph of a rational function?

Back

A hole occurs in the graph of a rational function when a factor from the numerator cancels with a factor in the denominator.

Front

What is the significance of vertical asymptotes?

Back

Vertical asymptotes indicate values of x where the function approaches infinity or negative infinity, typically where the denominator is zero.

Front

How do you find vertical asymptotes?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What happens to the graph of a rational function at a vertical asymptote?

Back

At a vertical asymptote, the graph of the rational function will approach infinity or negative infinity.

Front

What is the relationship between the degrees 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 horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Front

What does it mean for a rational function to be undefined?

Back

A rational function is undefined at values of x that make the denominator equal to zero.