Rational Functions-Vertical Asymptotes and Holes

Front

What is the definition of an ASYMPTOTE?

Back

A line that a curve approaches, as it heads towards infinity.

Front

Where is there a hole on the graph of the function if x = -2?

Back

x = -2

Front

Find the vertical asymptote(s) of the function if VA: x = 4.

Back

x = 4

Front

What occurs when the denominator is one degree smaller than the numerator?

Back

oblique asymptote

Front

What is a vertical asymptote?

Back

A vertical line where a function approaches infinity or negative infinity.

Front

What is a hole in a rational function?

Back

A point where the function is undefined due to a common factor in the numerator and denominator.

Front

How do you find vertical asymptotes?

Back

Set the denominator equal to zero and solve for x.

Front

What is the significance of a hole in a graph?

Back

It indicates a removable discontinuity in the function.

Front

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

Back

The graph approaches the asymptote but never touches or crosses it.

Front

What is the relationship between the degrees of the numerator and denominator for horizontal asymptotes?

Back

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.