Exercises for Question Type 2: Determining whether two transformations are the same effect wise

Question 1

On the graph of y = x^{2}, a horizontal stretch by factor \frac{1}{8} is followed by a vertical stretch by factor m to return the graph to y = x^{2} . Find m .

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Question 2

The graph of y = x^{2} is transformed to y = a x^{2} by performing a horizontal compression of scale factor \frac{1}{6} . Find the value of a and describe the equivalent vertical transformation.

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Question 3

When the graph of y = x^{2} undergoes a horizontal stretch of scale factor 5, the equation becomes y = K x^{2} . Find K .

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Question 4

Prove in general that a horizontal stretch by scale factor k applied to y = x^{2} is equivalent to a vertical stretch by scale factor \frac{1}{k ^{2}} .

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Question 5

A transformation of y = x^{2} consists of a vertical stretch by a factor of 9 followed by a horizontal stretch by a factor of k, resulting in the same graph as a single horizontal stretch by a factor of 3 . Determine the value of k .

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Question 6

The question explores the effect of vertical and horizontal stretches on the base function y = x^{2} . Students are required to express the combined transformation algebraically and find the relationship between the stretch factors p and q .

A function y = x^{2} is first stretched vertically by a factor of p and then horizontally by a factor of q, resulting in the function y = 9 x^{2} . Determine the relationship between p and q .

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Question 7

Determine the vertical stretch factor that produces the same graph as applying a horizontal stretch of scale factor \frac{1}{5} to the graph of y = x^{2} .

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Question 8

Determine the horizontal stretch factor that produces the same graph as applying a vertical stretch of scale factor 25 to the graph of y = x^{2} .

Question 9

Verify that the graphs of y = (\frac{x}{4})^{2} and y = \frac{1}{16} x^{2} represent the same graph, and describe the transformation of y = x^{2} that each represents.

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Question 10

Determine the vertical stretch factor that produces the same graph as applying a horizontal stretch of scale factor 3 to the graph of y = x^{2} .

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Question 11

Determine the horizontal stretch factor that produces the same graph as applying a vertical shrink of scale factor 1/16 to the graph of y = x^{2} .

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Question 12

If the graph of y = x^{2} is scaled horizontally by a factor of k and the resulting graph has equation y = \frac{1}{49} x^{2}, find k .

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IB Mathematics Applications & Interpretation Question Type 2: Determining Whether Two Transformations Are the Same Effect Wise Exercises