# Test: Functions II - Ambitious

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Question 1:   Find the period of the function $f\left(x\right)=\mathrm{cos}\left(\frac{\theta }{3}\right)$
$2\pi$
$\frac{1}{3}\pi$
$6\pi$
$3\pi$
Question 2:   Find the period of the function $f\left(x\right)=-6\mathrm{cot}\left(3\theta +4\right)$
$7\pi$
$\frac{4}{3}\pi$
$\pi$
$\frac{\pi }{3}$
Question 3:   Find the period of the function $f\left(x\right)=2\mathrm{cos}\left(\frac{\theta }{2}\right)+5\mathrm{cos}\left(\frac{\theta }{3}\right)$
$4\pi$
$12\pi$
$6\pi$
$18\pi$
Question 4:   Find the period of the function $f\left(x\right)=\frac{1}{5}\mathrm{sin}\left(3\theta \right)+\frac{1}{4}\mathrm{sin}\left(\frac{\theta }{5}\right)$
$10\pi$
$\frac{2}{3}\pi$
$30\pi$
$5\pi$
Question 5:   Find the amplitude of the function $f\left(x\right)=3\mathrm{sin}\left(\frac{\theta }{15}\right)$
$3$
$30$
$6$
$1$
Question 6:   Find the amplitude of the function $f\left(x\right)=x+1$ for $0\le x<2$ and$f\left(x+n\right)=f\left(x\right)$ for any integer.
$1$
$2$
$3$
$0$
Question 7:   Find the inverse of the function $f\left(x\right)=2{e}^{x}$.
${f}^{-1}\left(x\right)=\frac{1}{2}\mathrm{ln}x$
${f}^{-1}\left(x\right)=\frac{1}{2}{e}^{x}$
${f}^{-1}\left(x\right)=2\mathrm{ln}x$
${f}^{-1}\left(x\right)={e}^{\frac{1}{2}x}$
Question 8:   If the function is defined as $f\left(x\right)={x}^{2}+ax+b$, find the coefficients $a$ and $b$ if $f\left(2\right)=3$ and $f\left(3\right)=7$
$\left\{\begin{array}{l}a=0\\ b=\frac{1}{2}\end{array}$
$\left\{\begin{array}{l}a=1\\ b=-1\end{array}$
$\left\{\begin{array}{l}a=-1\\ b=1\end{array}$
$\left\{\begin{array}{l}a=1\\ b=2\end{array}$
Question 9:   On the diagram below is a sketch of a function $f\left(x\right)$. Sketch a graph of $y=|f\left(x\right)|$

Question 10:   On the diagram below is a sketch of a function $f\left(x\right)$. Sketch graph of $y=-f\left(x\right)$