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The graph of $y = f(x)$ is shown on the grid below - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 1

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Question 18

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The graph of $y = f(x)$ is shown on the grid below. (a) On the grid above, sketch the graph of $y = f(x - 2)$. On the grid, graph A has been reflected to give grap... show full transcript

Worked Solution & Example Answer:The graph of $y = f(x)$ is shown on the grid below - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 1

Step 1

On the grid above, sketch the graph of $y = f(x - 2)$

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Answer

To sketch the graph of y=f(x2)y = f(x - 2), we need to apply a horizontal shift to the original graph of f(x)f(x). The transformation f(x2)f(x - 2) means that the entire graph will shift to the right by 2 units. Thus, each point on the graph of y=f(x)y = f(x) is moved from (x,y)(x, y) to (x+2,y)(x + 2, y). This will result in the vertex of the parabola being at (2,k)(2, k), where kk is the original value at the vertex. Ensure that the shape of the graph remains consistent with the original function.

Step 2

Write down the equation of graph B.

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Answer

Graph B is obtained by reflecting graph A in the x-axis. If the equation of graph A is y=g(x)y = g(x), then the equation of graph B will be y=g(x)y = -g(x). This reflects every point on graph A across the x-axis. Therefore, we express this as:

y=extfunctionofg(x)y = - ext{function of } g(x)

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