Generating...                               s20quiz01_n20

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

    Image s20quiz01_pick_plot0

    Image s20quiz01_pick_plot1

    Image s20quiz01_pick_plot2

    Image s20quiz01_pick_plot3

  2. Sketch the graph of $\displaystyle y={{1}\over{5^{\left\vert x\right\vert }}}$

    Image s20quiz01_pick_plot4

    Image s20quiz01_pick_plot5

    Image s20quiz01_pick_plot6

    Image s20quiz01_pick_plot7

  3. Solve the equation $\displaystyle 3^{x+5}={{1}\over{3}}$

    [ x = −6 ]

    [ x = 4 ]

    $\displaystyle \left[ x={{1}\over{729}} \right] $

    $\displaystyle \left[ x=-{{14}\over{3}} \right] $

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

    $\displaystyle \left[ x=-{{\sqrt{15}+3}\over{3}} , x={{\sqrt{15}-3}\over{3}} \right] $

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

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

    $\displaystyle \left[ x=-\sqrt{7}-3 , x=\sqrt{7}-3 \right] $

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

    $(-\infty,\infty)$

    $[$ −5 $,\infty)$

    [  − 5 ,  5 ]

    $[0,\infty)$

  6. Find the equation for the parabola shown below.

    Image s20quiz01_pick_plot8

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

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

    $\displaystyle y=-2\,x^2+4\,x+16$

    $\displaystyle y=2\,x^2-4\,x-16$

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

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

    [ x = 1 ]

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

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

  8. Solve the equation $\displaystyle 9^{x}\,3^{x+2} = ( 27) 3^{2\,x}$

    [ x = −1 ]

    [ x = 25 ]

    $\displaystyle \left[ x={{25}\over{8}} \right] $

    [ x = 1 ]

  9. Solve the equation $\displaystyle x^2\,e^{x}-5\,x\,e^{x}=0$

    $\displaystyle \left[ x=0 , x=e^5 \right] $

    [ x = 0 ,  x = 5 ]

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

    $\displaystyle \left[ x=e , x=e^5 \right] $

  10. Find the vertex of $\displaystyle -x^2+6\,x-8$.

    [ 3 ,  1 ]

    [  − 3 ,   − 1 ]

    [  − 3 ,  1 ]

    [ 3 ,   − 1 ]


Department of Mathematics
Last modified: 2026-10-28