Graphing Rational Functions Flashcard Review

Front

What is a rational function?

Back

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

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, provided that the numerator is not also zero at those points.

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 determine the horizontal asymptote of a rational function?

Back

1. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. 2. If the degrees are equal, the horizontal asymptote is y=\frac{a}{b} where a and b are the leading coefficients. 3. If the degree of the numerator is greater, there is no horizontal asymptote.

Front

What is the range of a rational function?

Back

The range of a rational function is all real numbers except for any horizontal asymptotes.

Front

Back

The function is shifted 8 units to the right and 2 units down.

Front

What does inverse variation mean?

Back

Front

What is the significance of holes in the graph of a rational function?

Back

Holes occur in the graph of a rational function at points where both the numerator and denominator are zero, indicating that the function is undefined at that point.

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.