1. Sketch the graph for

    $\displaystyle f(x) = \begin{cases} -x & \mbox{if $x < -2$} \\ x-3 & \mbox{if $ -2 \le x \le 2$} \\ 3-x & \mbox{if $ 2 < x$} \end{cases} $

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  2. Sketch the graph for

    $\displaystyle f(x) = \begin{cases} x+4 & \mbox{if $x < 1$} \\ x^2 & \mbox{if $ 1 \le x \le 5$} \\ -x-3 & \mbox{if $ 5 < x$} \end{cases} $

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  3. Solve the equation $\displaystyle \ln x=\ln \left(x+2\right)-2$

    $\displaystyle \left[ x=-{{2\,e^2}\over{e^2-1}} \right] $

    [ x = 0 ]

    $\displaystyle \left[ x={{2}\over{e^2-1}} \right] $

    [ x = 2 ]

  4. Let $f(x) = 4-x^2$ , and let $g(x) = \sqrt{x}$ . Find the domain of  ${f\circ g}$.

    $[0,\infty)$

    $[$ −2 $,\infty)$

    [  − 2 ,  2 ]

    $(-\infty,\infty)$

  5. Solve the equation $\displaystyle -2\,x^2-6\,x+4=0$.

    [ x = −2 ,  x =  − 1 ]

    $\displaystyle \left[ x=-{{\sqrt{17}-3}\over{2}} , x={{\sqrt{17}+3}\over{2}} \right] $

    $\displaystyle \left[ x=-{{\sqrt{17}+3}\over{2}} , x={{\sqrt{17}-3}\over{2}} \right] $

    $\displaystyle \left[ x=3-\sqrt{5} , x=\sqrt{5}+3 \right] $

  6. Sketch the graph of $\displaystyle y={{1}\over{3^{\left\vert x\right\vert }}}$

    Image s20quiz01_pick_plot8

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  7. Find the equation for the parabola shown below.

    Image s20quiz01_pick_plot12

    $\displaystyle y=-x^2+4\,x-3$

    $\displaystyle y=2\,x^2-8\,x+6$

    $\displaystyle y=-2\,x^2+8\,x-6$

    $\displaystyle y=x^2-4\,x+3$

  8. Sketch the graph of $\displaystyle 2\,x^2-8\,x+5$.

    Image s20quiz01_pick_plot13

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  9. Solve the equation $\displaystyle 2^{x}=3^{1-x}$

    $\displaystyle \left[ x={{1}\over{\ln 3+\ln 2}} \right] $

    $\displaystyle \left[ x={{1}\over{2}} \right] $

    $\displaystyle \left[ x={{\ln 3}\over{\ln 3+\ln 2}} \right] $

    [ x = 1 ]

  10. Solve the equation $\displaystyle {{5^{x+1}}\over{25^{x}}} = ( 125) {{1}\over{5^{2\,x}}}$

    [ x = 2 ]

    [ x = 124 ]

    $\displaystyle \left[ x={{775}\over{19}} \right] $

    [ x = −2 ]


Department of Mathematics
Last modified: 2025-07-24