Unit 2: Functions
Topic 2.8: Rational Functions Questions
Practice 20 exam-style questions for IB Math AA SL Topic 2.8. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1State2 marks
2026
State the domain and range of y = 1/x.
Markscheme and model answer locked
Unlock Question3Write down1 mark
2026
The curve y = (3x − 1)/(x + 5) has a single vertical asymptote. State its equation.
Markscheme and model answer locked
Unlock Question4Write down1 mark
2026
Write down the vertical asymptote of .
Markscheme and model answer locked
Unlock Question5Sketch1 mark
2026
Sketch the graph of , showing both asymptotes.
Markscheme and model answer locked
Unlock Question6Show that1 mark
2026
Show that the horizontal asymptote is .
Markscheme and model answer locked
Unlock Question7Write down1 mark
2026
The curve y = (3x − 1)/(x + 5) levels off as x grows large. State the equation of the line it approaches.
Markscheme and model answer locked
Unlock Question8Sketch2 marks
2026
The function f is defined by f(x) = (2x + 3)/(x − 1), where x ∈ ℝ, x ≠ 1.
Sketch the graph of y = f(x), clearly showing the asymptotes and the intercepts with the axes.
Sketch the graph of y = f(x), clearly showing the asymptotes and the intercepts with the axes.
Markscheme and model answer locked
Unlock Question9Sketch2 marks
2026
The function f is defined by f(x) = (1 − 2x)/(x + 3), where x ∈ ℝ, x ≠ -3.
Sketch the graph of y = f(x), clearly showing the asymptotes and the intercepts with the axes.
Sketch the graph of y = f(x), clearly showing the asymptotes and the intercepts with the axes.
Markscheme and model answer locked
Unlock Question10Sketch2 marks
2026
The function f is defined by f(x) = (3x − 6)/(x + 2), where x ∈ ℝ, x ≠ -2.
Sketch the graph of y = f(x), clearly showing the asymptotes and the intercepts with the axes.
Sketch the graph of y = f(x), clearly showing the asymptotes and the intercepts with the axes.
Markscheme and model answer locked
Unlock Question11Write down1 mark
2026
Write down the horizontal asymptote of .
Markscheme and model answer locked
Unlock Question12Write down2 marks
2026
Write down the equations of the two asymptotes of .
Markscheme and model answer locked
Unlock Question13Sketch2 marks
2025
Draw the graph of . Mark both asymptotes and both axis intercepts.
Markscheme and model answer locked
Unlock Question15Write down1 mark
2021
Let for . Write down the range of .
Markscheme and model answer locked
Unlock Question16Write down1 mark
2021
For , write down the equations of both asymptotes of its graph.
Markscheme and model answer locked
Unlock Question18Write down2 marks
2026
Write down the equations of the two asymptotes of y = 1/x.
Markscheme and model answer locked
Unlock Question19Sketch1 mark
2023
Draw the graph of , showing its behaviour near both axes.
Markscheme and model answer locked
Unlock Question20Choose1 mark
The graph of is translated 2 units left and 3 units up. Write down the new equation.
Markscheme and model answer locked
Unlock QuestionReady to practice Topic 2.8?
Get instant AI feedback on your answers, view detailed markschemes, and track your progress across all IB Math AA SL topics.