Unit 2: Functions

Topic 2.13: Rational functions (HL only) Questions

Practice 20 exam-style questions for IB Math AA SL Topic 2.13. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

11 mark
2026
A vertical asymptote occurs at x = a when:
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2State2 marks
2026
State the horizontal asymptote of (6x² − x)/(3x² + 2).
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3Show that1 mark
2026
Show that has vertical asymptotes at and .
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4State2 marks
2026
State the vertical and horizontal asymptotes of f(x) = (3x − 2)/(x + 4).
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51 mark
2026
A rational function with top degree 1 and bottom degree 1 has:
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61 mark
2026
f(x) = (3x)/(x − 2). As x → ∞, f(x) →
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71 mark
2026
Which has a horizontal asymptote y = 0?
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81 mark
2026
The slant asymptote of (x² )/(x − 3) is found by:
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91 mark
2026
(x² + x + 1)/(x) splits as:
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10Sketch3 marks
2026
Sketch the key features of f(x) = (x + 4)/(x − 2): asymptotes and intercepts.
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11Show that2 marks
2026
Show that has a slant asymptote .
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12Find2 marks
2026
Find the vertical asymptotes of g(x) = (x − 1)/(x² − 5x + 6).
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131 mark
2026
Horizontal asymptote of (x³ + 1)/(x² − 1):
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14Find3 marks
2026
Determine all asymptotes of f(x) = (2x + 3)/(x² + x − 2).
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151 mark
2026
The vertical asymptote(s) of 1/(x² + 1) are:
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16Find2 marks
2026
Find the oblique asymptote of f(x) = (x² + 2x − 3)/(x − 1).
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17Find3 marks
2026
Find all asymptotes of f(x) = (x² − 4)/(x + 3).
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18State2 marks
2026
State the x- and y-intercepts of f(x) = (x² − 1)/(x + 2).
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19Find3 marks
2026
f(x) = (3x² + 2)/(x). Find its asymptotes.
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201 mark
2026
Which function has NO slant asymptote?
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