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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify the hole in the function $$f(x) = \frac{(x-3)(x+2)}{(x-3)(x+1)}$$.
💡 Hint: Look for the factor that cancels in both numerator and denominator.
Question 2
Easy
For the function $$g(x) = \frac{(x-1)(x+2)}{(x-1)(x-4)}$$, what is the hole?
💡 Hint: Identify the canceled factor.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does a hole represent in a rational function's graph?
- A point of intersection
- A point where the function is undefined
- A maximum point
💡 Hint: Think about the definition of a hole.
Question 2
True or False: A hole can occur at any value of x?
- True
- False
💡 Hint: Remember the condition of factor cancellation.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Graph the function $$f(x) = \frac{(x-1)(x+2)}{(x-1)(x^2)}$$. Identify both the holes and the behavior as you approach.
💡 Hint: Don't forget to check both numerator and denominator for cancellation.
Question 2
Consider the function $$g(x) = \frac{x^3 - 6x^2 + 9x}{x^2 - 4}$$. Determine the holes and provide a detailed analysis of the graph.
💡 Hint: Factor thoroughly and analyze each component.
Challenge and get performance evaluation