Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 8 - 2010 - Paper 1
Question 8
Figure 1 shows a sketch of the curve with equation $y = f(x)$. The curve has a maximum point A at $(-2, 3)$ and a minimum point B at $(3, -5)$.
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Worked Solution & Example Answer:Figure 1 shows a sketch of the curve with equation $y = f(x)$ - Edexcel - A-Level Maths Pure - Question 8 - 2010 - Paper 1
Step 1
a) $y = f(x + 3)$
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Answer
To sketch the graph of y=f(x+3), we will perform a horizontal translation to the left by 3 units.
The maximum point A, originally at (−2,3), will now move to (−5,3).
The minimum point B, originally at (3,−5), will shift to (0,−5).
Thus, the new coordinates marked on the sketch are:
Maximum A at (−5,3)
Minimum B at (0,−5)
Label the coordinates on the graph.
Step 2
b) $y = 2f(x)$
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Answer
For the graph of y=2f(x), we will perform a vertical stretch of the graph by a factor of 2.
The maximum point A will now be at (−2,2imes3)=(−2,6).
The minimum point B will now be at (3,2imes−5)=(3,−10).
Label these coordinates on the graph as:
Maximum A at (−2,6)
Minimum B at (3,−10).
Step 3
c) Write down the value of a.
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Answer
To find the value of a in the equation y=f(x)+a, we know that this graph has a minimum at (3,0).
Since the minimum of f(x) is −5 at x=3, we set up the equation:
