Graph of a scaled secant function with its asymptotes, and counting solutions of a modulus equation
Graph of a scaled secant function with its asymptotes, and counting solutions of a modulus equation
IB Year 6 | Grade 12
8 marks
The function \(\mathrm{f}\) is given by \(\mathrm{f}(x)=3\sec3x\).
- On the grid below, sketch the graph of \(y=\mathrm{f}(x)\) for \(0\le x\le\pi\), stating the equations of its vertical asymptotes.[4]
- Write down the least positive value of \(x\) for which \(\mathrm{f}(x)=-3\).[2]
- Find the number of solutions of the equation \(\left|\mathrm{f}(x)\right|=4\) in the interval \(0\le x\le\pi\).[2]
Solution:
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Answer:(a) asymptotes \(x=\dfrac{\pi}{6},\ x=\dfrac{\pi}{2},\ x=\dfrac{5\pi}{6}\) (b) \(x=\dfrac{\pi}{3}\) (c) \(6\)
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