Sinusoidal Function Transformations

00:00 5 marks

Consider the sinusoidal function \(f(x) = 3\sin(x – \frac{\pi}{4}) + 2\). This function is a transformation of the basic sine function incorporating amplitude change, phase shift, and vertical shift. Answer the following parts:

Part a

2 minutes 2 marks

Question

Identify the amplitude of the function \(f(x) = 3\sin(x – \frac{\pi}{4}) + 2\).

Hint Hint

Hint

Recall that the amplitude is the absolute value of the coefficient of \(\sin(x)\).

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Part b

3 minutes 3 marks

Question

If the graph of \(f(x) = 3\sin(x – \frac{\pi}{4}) + 2\) is shifted 2 units to the left, write the new equation of the function.

Hint Hint

Hint

Apply a horizontal shift by replacing \(x\) with \(x + 2\) in the function.

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Complete Answer

\(f(x) = 3\sin((x+2) – \frac{\pi}{4}) + 2\)

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