The diagram shows the cubic graph of $y = f(x)$, with stationary points at $(2, 0)$ and $(0, -2)$ - Scottish Highers Maths - Question 4 - 2023
Question 4
The diagram shows the cubic graph of $y = f(x)$, with stationary points at $(2, 0)$ and $(0, -2)$.
On the diagram in your answer booklet, sketch the graph of $y = ... show full transcript
Worked Solution & Example Answer:The diagram shows the cubic graph of $y = f(x)$, with stationary points at $(2, 0)$ and $(0, -2)$ - Scottish Highers Maths - Question 4 - 2023
Step 1
Reflect in the y-axis
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Answer
To sketch y=2f(−x), start by reflecting the original graph y=f(x) in the y-axis. This means that all points (x,y) will transform to (−x,y).
Step 2
Apply vertical scaling
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Next, apply a vertical scaling of 2. This means that for each point (−x,y) on the reflected graph, the new point will be (−x,2y). Hence, the y-coordinates will be doubled.
Step 3
Sketch the final graph
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Answer
Finally, sketch the transformed graph using the adjustments made. The graph will now have the same shape but will be vertically stretched and reflected across the y-axis.
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