Unit 2: Functions

Topic 2.11: Transformations of Graphs Questions

Practice 20 exam-style questions for IB Math AA SL Topic 2.11. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Write down2 marks

2026

The equation

g (x) = 0

has roots

x = - 1

and

x = 5

only. Write down the roots of (i)

g (x - 3) = 0

and (ii)

g (- x) = 0

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2Describe2 marks

2026

Describe fully the transformation that maps y = f(x) onto y = f(x) − 5.

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3Describe2 marks

2026

Describe fully the transformations in y = f(x − 3) + 2.

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4Describe2 marks

2026

Describe fully the transformations in

y = f (x - 3) + 2

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5Write down2 marks

2026

The equation

p (x) = 0

has exactly three roots:

- 3

1

and

4

. Write down the roots of

p (2 x) = 0

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6Describe2 marks

2026

Describe fully the single transformation mapping y = f(x) to y = f(x − 6).

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7Describe2 marks

2026

Describe fully the transformation that maps y = f(x) onto y = −f(x).

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8Choose1 mark

What single move takes the graph of

y = f (x)

to the graph of

y = f (x - 6)

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9Choose1 mark

Describe fully the transformation that maps

y = f (x)

onto

y = f (x) + 7

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10Describe2 marks

2026

Describe fully the transformation that maps

y = f (x)

onto

y = f (x) - 5

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11Describe2 marks

2026

Describe fully the transformation that maps y = f(x) onto y = 5f(x).

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12Write down1 mark

2026

The graph of

y = f (x)

is reflected in the y-axis. Write down the equation of the new graph.

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13Describe2 marks

2026

Describe fully the single transformation mapping

y = f (x)

y = f (x - 6)

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14Describe2 marks

2026

Describe fully the transformation that maps

y = f (x)

onto

y = - f (x)

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15Write down1 mark

2026

The graph of y = f(x) is reflected in the y-axis. Write down the equation of the new graph.

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16Describe2 marks

2026

Describe fully the transformation that maps

y = f (x)

onto

y = 5 f (x)

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17Describe2 marks

2026

Describe fully the transformation that maps

y = f (x)

onto

y = f \frac{x}{2}

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18Describe2 marks

2026

Describe fully the transformation that maps

y = f (x)

onto

y = f (x + 4)

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19Find2 marks

2026

Write the transformation from

y = f (x)

y = f (x - 2) - 5

as a translation vector.

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20Choose1 mark

The graph of

y = f (x)

has a minimum at

(- 1, 4)

. Find the minimum of

y = f (x + 2) + 3

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