Unit 2: Functions
Topic 2.3: Transformations of Graphs Questions
Practice 12 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.
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Use your GDC to find the x-intercepts of f(x) = x² + x − 12.
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Find the y-intercept of f(x) = −3x + 8.
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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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Use your GDC to find the coordinates of the minimum point of f(x) = x² − 4x + 1.
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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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A projectile's height (m) is modelled by h(t) = 80t − 5t², where t is seconds after launch. Suggest GDC window settings (Xmin, Xmax, Ymin, Ymax) that show the entire flight.
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A bakery's daily profit ($) for selling x pies is P(x) = −x² + 24x − 80. Find both intercepts of P and explain what each means in the context of the bakery.
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A company's profit (thousand $) for x months of operation is P(x) = −0.5x² + 6x − 5. Use your GDC to answer the following.
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