The graph of $y = f(x)$ is shown on the grid below. (a) On the grid above, sketch the graph of $y = f(-x)$. Here is a sketch of the graph of $y = an^2 x$. The graph of $y = an^2 x$ is translated to give the graph of $y = g(x)$. Following the translation the point $Q$, shown on the graph above, moves to point $R$. Point $R$ has coordinates $(90, -5)$. (b) Find an expression for $g(x)$ in terms of $x$.

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The graph of $y = f(x)$ is shown on the grid below - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 2

Question 22

The graph of $y = f(x)$ is shown on the grid below. (a) On the grid above, sketch the graph of $y = f(-x)$. Here is a sketch of the graph of $y = an^2 x$. The gr... show full transcript

Worked Solution & Example Answer:The graph of $y = f(x)$ is shown on the grid below - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 2

Step 1

Sketch the graph of $y = f(-x)$

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Answer

To sketch the graph of $y = f(-x)$ , reflect the graph of $y = f(x)$ across the y-axis. If $f(x)$ crosses the y-axis at a certain point and has peaks and troughs, these will also mirror accordingly in the transformed function.

Step 2

Find an expression for $g(x)$ in terms of $x$

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Answer

The translation has moved point $Q(90, -5)$ to point $R$ . The change in the y-coordinate indicates how the graph has been positioned. Therefore, the function transformation can be represented as:

$g(x) = an^2igg(270 - xigg) - 5$

Here, the function is shifted to the right by 270 degrees and then translated downward by 5 units.

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