Understanding Limits of Rational Functions

The video tutorial explains how to determine the limit of a rational function as x approaches negative nine. It highlights the issue of direct substitution leading to a zero denominator and explores the possibility of simplifying the rational expression. The tutorial then delves into one-sided limits, showing how the function approaches positive infinity from both sides. Verification through tables and graphs confirms these results, and a graphical representation further illustrates the concept.

What issue arises when trying to find the limit of the rational function as x approaches negative nine?

• The numerator becomes zero.

• The function simplifies completely.

• The denominator becomes zero.

• The function becomes undefined.

Why can't the rational function be simplified in this case?

• The numerator and denominator are identical.

• The function is already in its simplest form.

• The numerator does not factor into binomials.

• The factors of the numerator do not cancel with the denominator.

What does the numerator approach as x approaches negative nine from the left?

• Positive infinity

• Negative infinity

• 34

• Zero

As x approaches negative nine from the left, what happens to the denominator?

• It approaches zero from the left.

• It approaches a negative constant.

• It approaches zero from the right.

• It approaches a positive constant.

What is the overall limit of the function as x approaches negative nine from the left?

• Zero

• Negative infinity

• Positive infinity

• Undefined

What does the numerator approach as x approaches negative nine from the right?

• 34

• Positive infinity

• Negative infinity

• Zero

As x approaches negative nine from the right, what happens to the denominator?

• It approaches a positive constant.

• It approaches a negative constant.

• It approaches zero from the right.

• It approaches zero from the left.

What is the overall limit of the function as x approaches negative nine from the right?

• Zero

• Positive infinity

• Negative infinity

• Undefined

What does the table and graph verification show about the function as x approaches negative nine?

• The function values remain constant.

• The function values decrease without bound.

• The function values increase without bound.

• The function values oscillate.

What conclusion can be drawn about the original limit of the function?

• It is undefined.

• It approaches positive infinity.

• It approaches negative infinity.

• It approaches zero.