- Sketch the graph of \(y=\sec x\) for \(0 \leqslant x \leqslant 2 \pi\).
- In your answer, identify all asymptotes and the coordinates of any maximum and minimum turning points. (2 marks)
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- Using set notation, state the domain and range of \(y=\sec x\). (1 mark)
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a.
b. \(\text{Domain:} \ x \in\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right) \cup\left(\frac{3 \pi}{2}, 2 \pi\right]\)
\(\text{Range:} \ y \in(-\infty,-1] \cup[1, \infty)\)
Show Worked Solution
a. \(\text{Draw}\ \ y=\cos\,x\ \ \text{to inform graph:}\)
\(\text{Minimum TPs:}\ (0,1), (2\pi, 1) \)
\(\text{Maximum TP:}\ (\pi, -1)\)
b. \(\text{Domain:} \ x \in\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right) \cup\left(\frac{3 \pi}{2}, 2 \pi\right]\)
\(\text{Range:} \ y \in(-\infty,-1] \cup[1, \infty)\)