Quick Check: Finding Discontinuities for Rational Functions

Front

What is a hole in a rational function?

Back

A hole occurs when a factor from the numerator cancels with a factor in the denominator.

Front

How do you identify a hole in a function?

Back

To identify a hole, look for values of x that make both the numerator and denominator equal to zero.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes in a rational function?

Back

Set the denominator equal to zero and solve for x.

Front

What happens to a function at a hole?

Back

At a hole, the function is undefined, but the limit exists.

Front

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

Back

A hole indicates a removable discontinuity, while a vertical asymptote indicates a non-removable discontinuity.

Front

If a rational function has a hole at x = 3, what does this imply?

Back

It implies that both the numerator and denominator have a factor of (x - 3).

Front

Can a rational function have both holes and vertical asymptotes?

Back

Yes, a rational function can have both holes and vertical asymptotes.

Front

What is the significance of the degree of the numerator and denominator?

Back

The degree helps determine the behavior of the function as x approaches infinity and the presence of vertical asymptotes.

Front

If the degree of the numerator is greater than the degree of the denominator, what happens?

Back

The function approaches infinity or negative infinity as x approaches the vertical asymptote.