Exercises for Question Type 3: Given a description of transformations, finding the appropriate transformed function

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Exercises for Question Type 3: Given a description of transformations, finding the appropriate transformed function - IB

Question 1

The student must determine the equation of a function after applying a sequence of three transformations: a reflection in the y -axis, a horizontal stretch, and a vertical translation.

Given the function f (x) = x, the following transformations are applied in order: a reflection in the y -axis; a horizontal stretch by a factor of 4; a translation up by 5 units. Determine the equation of the resulting function.

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Question 2

Given g (x) = lo g (x), apply the following transformations in the order shown: a vertical stretch by a factor of 2 a translation 1 unit to the right a reflection in the y -axis Write down an expression for the resulting function.

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Question 3

Given f (x) = ∣ x ∣, apply a reflection in the x -axis followed by a vertical compression by a factor of \frac{1}{2} . Write the equation of the transformed function.

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Question 4

Let f (x) = e^{x} . Translate it 3 units left, then reflect in the y -axis. Determine the resulting function.

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Question 5

Describe the transformations mapping y = sin x to y = 5 sin (2 x - 6) .

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Question 6

Describe the transformations that map the graph of y = sin x onto the graph of y = \frac{1}{4} sin (3 x) .

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Question 7

Let f (x) = \frac{3}{x} . Perform the transformations: translate 2 units upwards, stretch horizontally by a factor of 3, then translate 4 units to the left. Express the resulting function.

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Question 8

Describe the sequence of transformations to obtain y = - 3 cos (4 (x + \frac{π}{3})) + 2 from y = cos x .

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Question 9

Given the function f (x) = x^{2}, apply the following transformations in order: stretch vertically by a factor of 3, translate 2 units to the right, then reflect in the x -axis. Write the equation of the transformed function.

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Question 10

Given f (x) = 7 (x + 5)^{2}, apply a vertical stretch by 4, then translate right 6 units, then stretch horizontally by factor 2. Find the resulting function.

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Question 11

Describe the transformations mapping y = x to y = - 2 x + 8 + 3 .

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Question 12

Describe the transformations from y = sin x to y = 2 sin (- \frac{x}{2}) - 1 .

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IB Mathematics Applications & Interpretation Question Type 3: Given a Description of Transformations, Finding the Appropriate Transformed Function Exercises