The graph of $y = f(x)$ is shown on the grid below - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 1
Question 18
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(x−2), we need to apply a horizontal shift to the original graph of f(x). The transformation 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) is moved from (x,y) to (x+2,y). This will result in the vertex of the parabola being at (2,k), where k 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), then the equation of graph B will be y=−g(x). This reflects every point on graph A across the x-axis. Therefore, we express this as: