Generating...                               s20quiz01_n1

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

    [ x = −2 ]

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

    [ x = 21 ]

    [ x = 6 ]

  2. Solve the equation $\displaystyle 5^{x-1}\,25^{x} = ( 125) 5^{6\,x}$

    $\displaystyle \left[ x=-{{4}\over{3}} \right] $

    $\displaystyle \left[ x={{63}\over{10}} \right] $

    [ x = −42 ]

    [ x = −4 ]

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

    [ 2 ,  1 ]

    [  − 2 ,  1 ]

    [  − 2 ,   − 1 ]

    [ 2 ,   − 1 ]

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

    $[$ −5 $,\infty)$

    [  − 5 ,  5 ]

    $[0,\infty)$

    $(-\infty,\infty)$

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

    $\displaystyle \left[ x=1-\sqrt{2} , x=\sqrt{2}+1 \right] $

    [ x = 1 ]

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

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

  6. Sketch the graph of $\displaystyle y=2^{\left\vert x\right\vert }$

    Image s20quiz01_pick_plot0

    Image s20quiz01_pick_plot1

    Image s20quiz01_pick_plot2

    Image s20quiz01_pick_plot3

  7. Sketch the graph for

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

    Image s20quiz01_pick_plot4

    Image s20quiz01_pick_plot5

    Image s20quiz01_pick_plot6

    Image s20quiz01_pick_plot7

  8. If a linear function $f$ satisfies f(4) = 3 and f(2) = 1, find $f(x)$.

    y = x + 1

    y = x − 1

    $\displaystyle y={{3\,x}\over{4}}+{{1}\over{2}}$

    $\displaystyle y={{3\,x}\over{4}}-{{1}\over{2}}$

  9. Find the equation for the parabola shown below.

    Image s20quiz01_pick_plot8

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

    $\displaystyle y=2\,x-{{x^2}\over{2}}$

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

    $\displaystyle y={{x^2}\over{2}}-2\,x$

  10. 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 ]


Department of Mathematics
Last modified: 2025-09-14