1. Solve the equation $\displaystyle {{5^{x-1}}\over{25^{x}}} = ( {{1}\over{25}}) 5^{x}$

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

    [ x = 26 ]

    [ x = 1 ]

    $\displaystyle \left[ x=-{{13}\over{25}} \right] $

  2. Solve the equation $\displaystyle 3^{x-4}={{1}\over{3}}$

    [ x = 27 ]

    $\displaystyle \left[ x={{13}\over{3}} \right] $

    [ x = −5 ]

    [ x = 3 ]

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

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

    [ x = 1 ,  x = 2 ]

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

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

  4. Solve the equation $\displaystyle \ln x=\ln \left(x+1\right)-1$

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

    [ x = 1 ]

    [ x = 0 ]

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

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

    $[$ −5 $,\infty)$

    [  − 5 ,  5 ]

    $[0,\infty)$

    $(-\infty,\infty)$

  6. Find the vertex of $\displaystyle -x^2-4\,x-3$.

    [  − 2 ,  1 ]

    [ 2 ,   − 1 ]

    [  − 2 ,   − 1 ]

    [ 2 ,  1 ]

  7. Let $f(x) = \sqrt{x}-1$ , and let $g(x) = 25-x^2$ . Sketch the graph of  ${f\circ g}$.

    Image s20quiz01_pick_plot0

    Image s20quiz01_pick_plot1

    Image s20quiz01_pick_plot2

    Image s20quiz01_pick_plot3

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

    $\displaystyle \left[ x=-\sqrt{2} , x=\sqrt{2} \right] $

    $\displaystyle \left[ x=0 , x=e^2 \right] $

    $\displaystyle \left[ x=e , x=e^2 \right] $

    [ x = 0 ,  x = 2 ]

  9. Sketch the graph of $\displaystyle 2\,x^2-12\,x+19$.

    Image s20quiz01_pick_plot4

    Image s20quiz01_pick_plot5

    Image s20quiz01_pick_plot6

    Image s20quiz01_pick_plot7

  10. Sketch the graph for

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

    Image s20quiz01_pick_plot8

    Image s20quiz01_pick_plot9

    Image s20quiz01_pick_plot10

    Image s20quiz01_pick_plot11


Department of Mathematics
Last modified: 2026-03-05