Generating...                               s20quiz01_n3

  1. Solve the equation $\displaystyle 5^{x+4}=25$

    $\displaystyle \left[ x={{1}\over{25}} \right] $

    [ x = 6 ]

    [ x = −2 ]

    [ x = 21 ]

  2. Sketch the graph for

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

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  3. Solve the equation $\displaystyle x^2\,e^{x}-3\,x\,e^{x}=0$

    [ x = 0 ,  x = 3 ]

    $\displaystyle \left[ x=e , x=e^3 \right] $

    $\displaystyle \left[ x=0 , x=e^3 \right] $

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

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

    Image s20quiz01_pick_plot4

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  5. Solve the equation $\displaystyle {{5^{x-2}}\over{25^{x}}} = ( 125) 5^{x}$

    $\displaystyle \left[ x=-{{127}\over{2}} \right] $

    [ x = 3175 ]

    $\displaystyle \left[ x=-{{5}\over{2}} \right] $

    [ x = −5 ]

  6. Solve the equation $\displaystyle -2\,x^2+5\,x-3=0$.

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

    $\displaystyle \left[ x=-{{\sqrt{37}+5}\over{2}} , x={{\sqrt{37}-5}\over{2}} \right] $

    $\displaystyle \left[ x=3 , x=-{{1}\over{2}} \right] $

    $\displaystyle \left[ x=-{{3}\over{2}} , x=-1 \right] $

  7. Let $f(x) = 25-x^2$ , and let $g(x) = \sqrt{x}$ . Find the domain of  ${f\circ g}$.

    $(-\infty,\infty)$

    $[$ −5 $,\infty)$

    $[0,\infty)$

    [  − 5 ,  5 ]

  8. Find the vertex of $\displaystyle 2\,x^2-12\,x+19$.

    [  − 3 ,  1 ]

    [  − 6 ,  2 ]

    [ 6 ,  2 ]

    [ 3 ,  1 ]

  9. Solve the equation $\displaystyle 2^{x}=7^{1-x}$

    $\displaystyle \left[ x={{\ln 7}\over{\ln 7+\ln 2}} \right] $

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

    $\displaystyle \left[ x={{1}\over{\ln 7+\ln 2}} \right] $

    [ x = 1 ]

  10. Sketch the graph for

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

    Image s20quiz01_pick_plot8

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Department of Mathematics
Last modified: 2026-07-16