Graph Transformations

00:00 5 marks

The graph of \(y = f(x)\) is shown below. The points A(-2, 0), B(0, 4), C(2, 0) and D(4, -2) lie on the curve.

(a) On the same axes, sketch the graph of \(y = f(x+2)\). Indicate the coordinates of the images of points A, B, C and D. [3]
(b) On a different set of axes, sketch the graph of \(y = -f(x)\). Indicate the coordinates of the images of points A, B, C and D. [2]

Part a

5 minutes 3 marks

Question

On the same axes, sketch the graph of \(y = f(x+2)\). Indicate the coordinates of the images of points A, B, C and D. [3]

Hint Hint

Hint

Shift each point 2 units to the left: replace x by (x-2).

Answer Answer
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Explanation Explanation

Answer Answer

Complete Answer

The graph shifts 2 units left. Coordinates: A'(-4, 0), B'(-2, 4), C'(0, 0), D'(2, -2).

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Part b

5 minutes 2 marks

Question

On a different set of axes, sketch the graph of \(y = -f(x)\). Indicate the coordinates of the images of points A, B, C and D. [2]

Hint Hint

Hint

Reflect the graph in the x-axis by negating each y-coordinate.

Answer Answer
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Explanation Explanation

Answer Answer

Complete Answer

Reflecting in the x-axis gives: A”(-2, 0), B”(0, -4), C”(2, 0), D”(4, 2).

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