What are the restrictions on our solutions for a rational equation

The video tutorial explains the importance of domain restrictions in solving rational equations, focusing on asymptotes and holes. It highlights how these features affect the graph of a rational function and introduces the concept of extraneous solutions, which arise when solutions correspond to undefined values. The tutorial also covers the process of identifying asymptotes and holes in equations and emphasizes the role of factoring in distinguishing between them.

What is the primary reason for having domain restrictions in rational equations?

• To avoid undefined values

• To ensure the graph is continuous

• To make the equation linear

• To simplify the equation

How can you identify a hole in the graph of a rational equation?

• By finding where the graph crosses the x-axis

• By locating the vertical asymptotes

• By identifying open circles on the graph

• By checking where the graph is horizontal

What happens when a value makes the denominator of a rational equation zero?

• The value is part of the solution

• The equation becomes linear

• The graph becomes a straight line

• The value is undefined

What is an extraneous solution in the context of rational equations?

• A solution that simplifies the equation

• A solution that makes the equation linear

• A solution that does not satisfy the original equation

• A solution that satisfies the equation

Why is it important to check solutions against original constraints?

• To ensure all solutions are extraneous

• To verify the solutions are valid

• To make the equation more complex

• To find more solutions