Unit 2: Functions
Topic 2.4: Key Features of Graphs Questions
Practice 16 exam-style questions for IB Math AA SL Topic 2.4. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Write down1 mark
2026• Aimnova practice — 2.4.2
Write down the equation you would solve to find where y = 2x − 1 meets y = x + 5.
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2026• Aimnova practice — 2.4.1
The graph of f has its lowest point at (2, −7). Write down the minimum value of f.
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2026• Aimnova practice — 2.4.1
State the zeros of f(x) = (x + 1)(x − 6).
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2026• Aimnova practice — 2.4.2
The graphs of y = f(x) and y = g(x) meet at the point (4, 7). Write down the value of (a) f(4) and (b) g(4).
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2026• Aimnova practice — 2.4.1
For the graph of y = 3 − 2/(x + 4): (a) state the vertical asymptote, and (b) state the horizontal asymptote.
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2026• Aimnova practice — 2.4.1
A quadratic has vertex (3, 5) and opens downward. (a) State its maximum value. (b) State the equation of its axis of symmetry.
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2026• Aimnova practice — 2.4.1
Consider f(x) = x² − 6x + 8. (a) Find the coordinates of the minimum point. (b) State the interval on which f is decreasing.
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2026• Aimnova practice — 2.4.2
Find the coordinates where y = 2ˣ meets the line y = 8.
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2026• Aimnova practice — 2.4.2
Find the coordinates where the graph of y = x² − 1 meets the line y = 3.
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2026• Aimnova practice — 2.4.2
Find the coordinates where the line y = x + 2 meets the parabola y = x².
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2026• Aimnova practice — 2.4.1
For the graph of y = 4/(x − 1): (a) write down the vertical asymptote, and (b) state the value y approaches as x → ∞.
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2026• Aimnova practice — 2.4.2
The curves y = x² − 4x and y = x intersect. (a) Show that their x-coordinates satisfy x² − 5x = 0. (b) Find the coordinates of the intersection points.
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2026• Aimnova practice — 2.4.1
The graph of y = f(x) passes through (0, 4), has a local maximum at (2, 8) and a local minimum at (5, 1). (a) Write down the y-intercept. (b) Write down the maximum value. (c) State the x-value at which the minimum occurs.
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2026• Aimnova practice — 2.4.1
A function f is increasing for x < −2 and for x > 1, and decreasing for −2 < x < 1. State the x-coordinate of (a) its local maximum and (b) its local minimum.
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2026• Aimnova practice — 2.4.2
Find the coordinates where y = 6/x meets y = x + 1.
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2026• Aimnova practice — 2.4.2
On a GDC, y = x³ − 2x and y = 1 are graphed and the intersect tool gives x = 1.52 (3 s.f.). State the equation in x that this value solves.
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