Math 2 Exam I Practice Answers

These are the answers to the Exam I Practice.

P Level

    1. \([-2,4)\)
    2. \([1,6)\)
    3. \((1,2)\cup(3,4)\)

  2. The domain is \((-4,-3)\cup[-2,0)\cup[2,3)\) and the range is \((-2,-1)\cup(1,4]\)

    1. \(-\frac{1}{3}\)
    2. \(2\)
    1. Both domains are \((-1,4)\)
    2. Both domains are \([5,6)\)
    1. \((-\infty,\infty)\)
    2. \((-\infty,\infty)\)
    3. \((-\infty,4]\)
    4. \((-\infty,-3)\cup(-3,\infty)\)

  6. \((-\infty,-2)\cup(4,5)\)

  7. \((5,-2)\)

  8. \(\langle 2,-1\rangle\)

  9. \(\langle 6, 2\rangle\)

  10. Center is \((2,-9)\) and radius is \(4\)

  11. \(\langle 1,\frac{4}{3}\rangle\) or \(\langle 3,4\rangle\)

  12. \(\langle -3,2\rangle\)

  13. Slope is \(-\frac{3}{4}\)

  14. Slope of \(\frac{1}{3}\)

  15. Domain is \((2,\infty)\) and the range is \((-2,9]\)

C Level

    1. \([-2,5]\)
    2. \(\{\}\)
    3. \((1,5]\)
    1. \(y=4\) and \(x=\frac{4}{3}\)
    2. \(y=11\) and \(x=-\frac{11}{2}\)
    3. \(y=-5\) and \(x=1\)
    1. \(\mathcal{D}\left(\frac{f}{g}\right)=(-1,4)\), \(\mathcal{D}\left(\frac{g}{f}\right)=\left(-1,\frac{1}{2}\right)\cup\left(\frac{1}{2},3\right)\cup(3,4)\)
    2. \(\mathcal{D}\left(\frac{f}{g}\right)=\left[5,\frac{11}{2}\right)\cup\left(\frac{11}{2},6\right)\), \(\mathcal{D}\left(\frac{g}{f}\right)=(5,6)\)

  4. \(f=\frac{c\circ b}{a}+e\circ(b+d)\)

  1. \(\left(-\frac{3}{\sqrt{34}},\frac{5}{\sqrt{34}}\right)\)

  2. \(\left(-\frac{1}{2},\frac{5}{2}\right)\)

  3. \(f^{-1}(x)=\sqrt[3]{x-1}-2\) Domain of the inverse and range of the inverse is \((-\infty,\infty)\)

B Level

    1. \([1,4]\)
    2. \((-4,4]\)

  2. \(\ell(t)=\begin{cases}\frac{t}{10}\langle 2,11 \rangle+(2,-1)&\text{ if }0\leq t\leq 10\\ \frac{t-10}{2}\langle 7,-10 \rangle+(4,10) &\text{ if }10<t\leq 12\end{cases}\)

  3. \(\left(-\frac{3}{\sqrt{26}}+3,\frac{15}{\sqrt{26}}+11 \right)\) and \(\left(\frac{3}{\sqrt{26}}+3,-\frac{15}{\sqrt{26}}+11 \right)\)

  4. \(\left(\frac{9}{5}+2,\frac{12}{5}\right)\)

  5. \((0,1)\cup \left(\frac{9}{2},\infty\right)\)

A Level

  1. \((f\circ g)(x)=\begin{cases}\frac{9}{2}x+15 &\text{ if } -4\leq x<-2\\\left(\frac{3}{2}x+5\right)^2-1 &\text{ if } 0\leq x\leq 1\\ \left(-x+9\right)^2-1 &\text{ if } 2< x\leq 4\\ \end{cases}\)

    1. \((-2,0)\cup(2,4]\)
    2. \((-4,-3]\)
    3. \((-3,1)\cup(1,3]\)
    1. The sketches \(f\) and \(f^{-1}\) are below
    2. \(f^{-1}(x)=\begin{cases}\sqrt{x}&\text{ if }0\leq x\leq 1\\-\sqrt{x}&\text{ if }1<x<4\\-\sqrt{x}&\text{ if }9\leq x<16\end{cases}\)

  1. \(y=\frac{13}{9}x-\frac{19}{9}\).

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