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Higher November 2021 Unit 2 Q15

WJECHigherCurrent spec3 marksGraphical Transformations

15. The following diagram shows a sketch of the curve \(y = f(x)\).

Sketch of y = f(x): the curve crosses the x-axis at −8 and the y-axis at 3, rising to a maximum and then falling

In each of the following questions, the graph of \(y = f(x)\) has been transformed.

(a)
Transformed curve, same shape as y = f(x), passing through the origin

Circle the only possible equation of the transformed curve. [1]

\(y = f(x) - 3\)     \(y = f(x - 3)\)     \(y = \tfrac{1}{3} f(x)\)     \(y = f(x + 3)\)     \(y = f(x) + 3\)

(b)
Transformed curve: crosses the x-axis at −8 and the y-axis at −3, falling to a minimum and then rising

Circle the only possible equation of the transformed curve. [1]

\(y = f(x) - 6\)     \(y = -f(x)\)     \(y = f(x + 8)\)     \(y = f(x) + 6\)     \(y = f(-x)\)

(c)
Transformed curve, same shape as y = f(x), crossing the x-axis at 2

Circle the only possible equation of the transformed curve. [1]

\(y = f(x) + 10\)     \(y = f(x + 10)\)     \(y = -4f(x)\)     \(y = f(x - 10)\)     \(y = f(x) - 10\)

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