Discontinuities- Holes and Vertical Asymptotes

Front

What is the equation of a vertical asymptote?

Back

x =

Front

When do holes occur in a rational function?

Back

When a factor in the denominator cancels with a factor in the numerator.

Front

What is the definition of an asymptote?

Back

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

Front

What is determined by just looking at the denominator of a rational function?

Back

Vertical asymptote.

Front

What is a hole in a rational function?

Back

A point where the function is undefined due to a factor canceling.

Front

How do you find vertical asymptotes?

Back

Set the denominator equal to zero and solve for x.

Front

What is the difference between a hole and a vertical asymptote?

Back

A hole occurs when a factor cancels; a vertical asymptote occurs when the denominator is zero but does not cancel.

Front

What does it mean for a function to approach an asymptote?

Back

The function gets closer to the asymptote value as x approaches a certain value.

Front

Can a function have both holes and vertical asymptotes?

Back

Yes, a function can have both if it has factors that cancel and factors that do not.

Front

What is the significance of vertical asymptotes in graphing?

Back

They indicate where the function will not exist and where the graph will approach infinity.