Evaluate the limit of a rational expression with a hole

The video tutorial discusses the challenges of using direct substitution in rational expressions when the denominator becomes zero. It explains the importance of factoring to resolve these issues and how it helps identify holes in graphs. The tutorial further explores graph behavior and limits at these holes, emphasizing the continuity from both sides. Finally, it demonstrates graphing the expression x-4 and verifying results using a calculator.

What is the issue with using direct substitution in rational expressions when the denominator becomes zero?

• It makes the expression continuous.

• It simplifies the expression.

• It creates a jump discontinuity.

• It results in an undefined expression.

What does factoring the denominator of a rational expression help to identify?

• A point of intersection.

• A horizontal asymptote.

• A vertical asymptote.

• A hole in the graph.

When a graph approaches a hole from both sides, what is it important to check?

• That it approaches the same value.

• That it forms a vertical asymptote.

• That it creates a jump discontinuity.

• That it intersects the x-axis.

After simplifying a rational expression, what method can be used to find the value at a hole?

• Direct substitution.

• Using a calculator to find the limit.

• Finding the derivative.

• Graphing the original expression.

How can you verify the result of a simplified rational expression?

• By checking for asymptotes.

• By solving for x.

• By finding the derivative.

• By graphing the expression.