Unit 2: Functions
Topic 2.3: Transformations of Graphs Questions
Practice 20 exam-style questions for IB Math AI SL Topic 2.3. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1find3 marks
Use your GDC to find the x-intercepts of f(x) = x² + x − 12.
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Use your GDC to find the coordinates of the minimum point of f(x) = x² − 4x + 1.
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The function k is defined by k(x) = 10/(x + 2) + 1, x ≠ −2. Write down the equations of the vertical and horizontal asymptotes of the graph of k, and find the y-intercept.
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A parabola is given by y = −3x² + 18x − 5. Where is its highest point?
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Two lines have equations f(x) = 2x + 1 and g(x) = −3x + 16. Use your GDC to find the point where they cross.
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Use your GDC to find the coordinates of the minimum point of f(x) = x² − 6x + 5.
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Where does the graph of f(x) = x² − 2x − 15 meet the horizontal axis?
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Find the y-intercept of f(x) = −3x + 8.
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2026
Write down the greatest value of .
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A diver's height above water (in metres) is modelled by h(t) = −5t² + 4t + 9, where t is seconds after jumping. State the diver's starting height above the water.
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2026
Sketch the graph of , showing the asymptote and the -intercept.
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Use your GDC to find the maximum point of f(x) = −2x² + 12x − 10.
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Two lines have equations f(x) = 3x − 2 and g(x) = −x + 6. Use your GDC to find their point of intersection.
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Find the x-intercepts of g(x) = 2x² + x − 6.
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A boat's speed v (in km/h) is modelled by v(t) = 18 − 0.6t, where t is hours after midnight. Find the time at which the boat stops, and interpret your answer in context.
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The function f is defined by f(x) = x² − 4x + 1. Using your graphic display calculator, find the y-intercept of the graph of f, the x-intercepts correct to three significant figures, and the coordinates of its vertex.
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The function g is defined by g(x) = 2ˣ − 5. Using your graphic display calculator, find the y-intercept of the graph of g, the x-intercept correct to three significant figures, and the equation of the horizontal asymptote.
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