Exercises for Question Type 4: Visually applying simple matrix transformations

Question 1

Skill question

A square of side length 2 is subjected to a horizontal stretch factor 3 and a vertical stretch factor 4. Calculate the area of the image.

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Question 2

Skill question

The transformation of functions involves horizontal and vertical stretches and translations. For horizontal transformations inside the function argument, the order of operations typically follows the reverse of standard arithmetic if working from the outside in, or can be determined by factorizing the expression $f (a x - b)$ as $f (a (x - \frac{b}{a}))$ .

A function $f (x)$ is transformed to $g (x) = 9 f (2 x - 4) + 3$ . List, in order, a possible sequence of transformations applied to $f (x)$ to obtain $g (x)$ .

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Question 3

Skill question

A rectangle has vertices $(1, 1), (4, 1), (4, 3), (1, 3)$ . Reflect it in the line $x = 2$ , then apply a vertical stretch by factor 2. Find the final coordinates.

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Question 4

Skill question

Determine the single $2 \times 2$ matrix representing first an enlargement by factor 2 about the origin, then a reflection in the line $y = 0$ .

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Question 5

Skill question

Find the $2 \times 2$ matrix representing first a horizontal stretch by factor 3, then a vertical stretch by factor 2 in the plane.

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Question 6

Skill question

The mapping $T : (x, y) \mapsto (3 x + 1, 3 y - 2)$ . (a) Describe $T$ as an enlargement followed by a translation. (b) Describe $T$ as a horizontal stretch, a vertical stretch, and translations.

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Question 7

Skill question

Let $f (x) = x^{2}$ . Perform a horizontal stretch by factor $\frac{1}{2}$ , then a vertical stretch by factor 4. Write down the equation of the transformed function $g (x)$ .

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Question 8

Skill question

A function $f (x)$ is first subjected to a vertical stretch by factor 5 about the $x$ -axis, then a horizontal stretch by factor 2 about the $y$ -axis. Write the equation of the resulting function in terms of $f$ .

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Question 9

Skill question

Given point $A (2, 1)$ , apply an enlargement of scale factor $3$ centred at the origin, then translate by vector $(03)$ . Find the coordinates of the image $A^{'}$ .

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Question 10

Skill question

Triangle $A B C$ has vertices $A (1, 2)$ , $B (3, 1)$ and $C (2, 4)$ . Reflect it in the $y$ -axis, then enlarge by a scale factor of 2 about the origin. Find the coordinates of $A^{'}$ , $B^{'}$ , $C^{'}$ .

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Question 11

Skill question

The function $f (x) = \frac{1}{x}$ is mapped to $h (x) = - \frac{1}{x} + 2$ . Describe the sequence of transformations that takes $f$ to $h$ .

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Question 12

Skill question

The graph of $y = f (x)$ is transformed to $y = g (x) = - 2 f (3 x) + 5$ . Describe each transformation in order.

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IB Mathematics Applications & Interpretation Question Type 4: Visually Applying Simple Matrix Transformations Exercises