Practice Horizontal Asymptotes (4.2) - Rational Functions - IB 10 Mathematics

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10 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
4 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the horizontal asymptote of f(x) = (3)/(x + 1)?
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Look at the degrees of the polynomial in the numerator and denominator.
Question 2.
Identify the horizontal asymptote for f(x) = (x)/(x² + 1).
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Compare the degrees.
3Question 3.
Which of the following describes a horizontal asymptote?
- y = 0 when f(x) approaches infinity
- f(x) touches y
- x approaches negative infinity only
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Recall what happens to the graph as x gets very large.
4Question 4.
True or False: A rational function can cross its horizontal asymptote.
- True
- False
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Think about graph behavior around asymptotes.
Question 5.
Provide the horizontal asymptote for the following function: f(x) = (6x² + 8)/(3x² + 2x + 1). Explain your reasoning behind the answer.
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Review leading coefficients.
Question 6.
Evaluate the rational function f(x) = (5x^4 – 2)/(7x^3 + 4). Determine its horizontal asymptote and justify your conclusion.
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Focus on the degree comparison again.

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