Graphing Rational Functions Review

Front

What is a Vertical Asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

Front

What is the domain of a rational function?

Back

The domain of a rational function is the set of all real numbers except for values that make the denominator zero.

Front

What is the range of a rational function?

Back

The range of a rational function is the set of all real numbers except for values that the function cannot output, often determined by horizontal asymptotes.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving for x.

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. It indicates the end behavior of the function.

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes can be found by analyzing the degrees of the numerator and denominator of the rational function.

Front

What is the significance of asymptotes in graphing?

Back

Asymptotes help determine the behavior of the graph near certain values and guide the overall shape of the graph.

Front

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

Front

What does it mean if a function has no vertical asymptotes?

Back

If a function has no vertical asymptotes, it means that the denominator does not equal zero for any real number, indicating the function is defined for all real numbers.

Front

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

Back

Holes occur when a factor in the numerator and denominator cancels out, indicating a point where the function is not defined.