Methods2025 Exam 1 · Q3Tech-free6 marks

Range, zeros and graph of a cosine function

Let $f: [0, 2\pi] \to \R, f(x) = 2\cos(2x) + 1$ .

State the range of $f$ .

1 mark

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Solve $f(x) = 0$ for $x$ .

3 marks

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Sketch the graph of $y = f(x)$ for $x \in \left[\frac{\pi}{2}, \frac{3\pi}{2}\right]$ on the axes below.

Label the endpoints with their coordinates.

Blank grid for sketching: x-axis marked at pi/2, pi, 3pi/2 and 2pi, y-axis marked from -2 to 3, with origin O.

2 marks

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