Practice Holes In The Graph (5) - Rational Functions - IB 10 Mathematics – Group 5, Algebra

Practice: Holes in the Graph

Lesson 5Rational Functions

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9 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Identify the hole in the function $f(x) = \frac{(x-3)(x+2)}{(x-3)(x+1)}$ .
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Look for the factor that cancels in both numerator and denominator.
Question 2.
For the function $g(x) = \frac{(x-1)(x+2)}{(x-1)(x-4)}$ , what is the hole?
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Identify the canceled factor.
3Question 3.
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
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Think about the definition of a hole.
4Question 4.
True or False: A hole can occur at any value of x?
- True
- False
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Remember the condition of factor cancellation.
Question 5.
Graph the function $f(x) = \frac{(x-1)(x+2)}{(x-1)(x^2)}$ . Identify both the holes and the behavior as you approach.
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Don't forget to check both numerator and denominator for cancellation.
Question 6.
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.
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Factor thoroughly and analyze each component.

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