Exercises for Question Type 1: Drawing the effect of single transformations on a graph

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Exercises for Question Type 1: Drawing the effect of single transformations on a graph - IB

Question 1

For f (x) = x^{2} - 3, sketch the graph of the function after a vertical stretch by factor 5 . Label the vertex and two more points.

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Question 2

Determine whether applying a horizontal stretch of factor \frac{1}{4} to f (x) = x^{2} yields the same graph as a vertical stretch by factor 16. Provide a short proof. [4 marks]

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Question 3

Sketch the graph of the function obtained by a horizontal compression of factor 3 of f (x) = x^{2} . Label the vertex and two other symmetric points.

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Question 4

Given f (x) = x^{2} + 1, sketch the graph of the function obtained by applying a vertical stretch of factor 3 to f . Label the new vertex and two other points.

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Question 5

Sketch the graph of g (x) = 4 (x^{2} - 2) . Clearly label the vertex and two additional points on each side of the axis of symmetry.

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Question 6

Determine whether the following two transformations of f (x) = x^{2} produce the same graph: A horizontal stretch by factor 4 A vertical stretch by factor 16 Explain your reasoning.

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Question 7

For f (x) = x^{2} - 1, determine whether a horizontal stretch by a scale factor of 5 of the graph of f is equivalent to a vertical stretch by a scale factor of 25. Show all steps.

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Question 8

Let f (x) = x^{2} - 4 . Draw the graph of the function obtained by a horizontal stretch of factor 2 applied to f . Label the vertex and two other points.

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Question 9

Given f (x) = x^{2} + 2, draw the graph of the function after reflecting f in the x -axis. Label key points.

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Question 10

Determine whether a horizontal compression by a factor of 3 of f (x) = x^{2} is equivalent to a vertical stretch by a factor of 9. Justify your answer.

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Question 11

Is a horizontal compression by factor 2 of f (x) = x^{2} the same transformation as a vertical stretch by factor 4? Justify your answer.

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Question 12

Sketch the graph of g (x) = 2∣ x ∣ by applying a vertical stretch of factor 2 to f (x) = ∣ x ∣ . Label the vertex and two other points.

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Question 13

For f (x) = x^{2}, determine whether a horizontal stretch by factor \frac{1}{2} and a vertical stretch by factor 4 produce the same transformed graph. Justify your answer.

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IB Mathematics Applications & Interpretation Question Type 1: Drawing the Effect of Single Transformations on a Graph Exercises