Rational Functions and Asymptotes

Front

What is a rational function?

Back

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines that a graph approaches but never touches or crosses, occurring where the denominator of a rational function equals 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 are horizontal asymptotes?

Back

Horizontal asymptotes are lines that a graph approaches as x approaches positive or negative infinity, indicating the behavior of the function at extreme values.

Front

How do you find horizontal asymptotes for rational functions?

Back

For rational functions, compare the degrees of the numerator and denominator: If the degree of the numerator is less, y=0; if equal, y= leading coefficient of P / leading coefficient of Q; if greater, no horizontal asymptote.

Front

What is a hole in a rational function's graph?

Back

A hole occurs in the graph of a rational function at a point where a factor in the numerator and denominator cancels out.

Front

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

Back

To find x-intercepts, set the numerator of the rational function equal to zero and solve for x.

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient determines the end 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 includes all real numbers except where the denominator equals 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 affected by vertical and horizontal asymptotes.