Unit 2: Functions

Topic 2.4: Key Features of Graphs Questions

Practice 20 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.

1State2 marks

2026

State the zeros of

f (x) = (x + 1) (x - 6)

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2Write down2 marks

2026

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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3Find1 mark

2021

Let

f (x) = x^{3} + 2 x

. Use your GDC to find

f^{- 1} (5)

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4Write down1 mark

2026

Write down the equation you would solve to find where

y = 2 x - 1

meets

y = x + 5

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5Write down1 mark

2026

The graph of f has its lowest point at (2, −7). Write down the minimum value of f.

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6Write down2 marks

2026

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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7State2 marks

2026

State the zeros of f(x) = (x + 1)(x − 6).

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8Write down3 marks

2026

Write down the coordinates of the local maximum, the local minimum and the

y

-intercept.

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9Find1 mark

2021

The exponential curve

y = e^{x}

and the straight line

y = 3 - x

cross once. With a GDC, determine the

x

-value at that crossing.

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10Find1 mark

2023

Give the coordinates of the point at which the curve

y = \frac{2 x - 5}{x + 1}

crosses the horizontal axis.

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11Find2 marks

2026

The function f is defined by f(x) = (6x − 8)/(3x + 2), x ≠ −2/3.

Find the value of

(i) the y-intercept;

(ii) the x-intercept.

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12Write down1 mark

2026

Write down the equation you would solve to find where y = 2x − 1 meets y = x + 5.

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13Find1 mark

2026

Find the equation of the vertical asymptote.

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14Find1 mark

2023

Give the coordinates of the point at which the curve

y = \frac{x - 3}{x + 2}

crosses the vertical axis.

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15Find4 marks

2026

Use your calculator to find the coordinates of the points where the graphs of

f

and

g

intersect.

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16Sketch3 marks

2023

Sketch

y = ln (x^{2} + 1) - x

for

- 2 \leq x \leq 4

, labelling the stationary point and both endpoints.

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17Find3 marks

2026

Find the coordinates where the graph of y = x² − 1 meets the line y = 3.

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18Explain1 mark

2026

Explain what this tells you about the factorisation of

f (x)

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19Find2 marks

2026

Find the coordinates where y = 2ˣ meets the line y = 8.

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20Find3 marks

2026

Find the coordinates where the graph of

y = x^{2} - 1

meets the line

y = 3

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