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The diagram shows part of the graph of the function $y = p \, ext{cos} \, qx + r$ - Scottish Highers Maths - Question 4 - 2015

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Question 4

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The diagram shows part of the graph of the function $y = p \, ext{cos} \, qx + r$. Write down the values of $p$, $q$ and $r$.

Worked Solution & Example Answer:The diagram shows part of the graph of the function $y = p \, ext{cos} \, qx + r$ - Scottish Highers Maths - Question 4 - 2015

Step 1

state the value of p

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Answer

The amplitude of the cosine function corresponds to the value of pp. From the graph, the peak is at y=4y = 4 and the trough is at y=−2y = -2, giving an amplitude of:

p = rac{4 - (-2)}{2} = 3

Step 2

state the value of q

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Answer

The period of the cosine function can be determined from the x-values at which the function completes one cycle. The graph completes a cycle from 00 to rac{ ext{π}}{2}, indicating that:

ext{Period} = rac{2 ext{π}}{q} Equating periods: rac{ ext{π}}{2} = rac{2 ext{π}}{q} Thus, solving for qq gives: q=4q = 4

Step 3

state the value of r

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Answer

The vertical shift of the cosine function is represented by rr. The midline of the graph can be found between the maximum and minimum values. Hence:

r = rac{4 + (-2)}{2} = 1

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