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

    Image s20quiz01_pick_plot0

    Image s20quiz01_pick_plot1

    Image s20quiz01_pick_plot2

    Image s20quiz01_pick_plot3

  2. Let $f(x) = \sqrt{x}+2$ , and let $g(x) = 9-x^2$ . Sketch the graph of  ${f\circ g}$.

    Image s20quiz01_pick_plot4

    Image s20quiz01_pick_plot5

    Image s20quiz01_pick_plot6

    Image s20quiz01_pick_plot7

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

    [ x = e ,  x = e ]

    [ x = 0 ,  x = e ]

    [ x = 0 ,  x = 1 ]

    [ x = −1 ,  x = 1 ]

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

    [ x = 3 ]

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

    [ x = 27 ]

    [ x = −5 ]

  5. Solve the equation $\displaystyle \ln x=\ln \left(x+2\right)-1$

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

    [ x = 2 ]

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

    [ x = 1 ]

  6. Solve the equation $\displaystyle 4^{x}=7^{-x-2}$

    [ x = −2 ]

    [ x = −1 ]

    $\displaystyle \left[ x=-{{2\,\ln 7}\over{\ln 7+\ln 4}} \right] $

    $\displaystyle \left[ x=-{{2}\over{\ln 7+\ln 4}} \right] $

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

    $(-\infty,\infty)$

    $[$ −2 $,\infty)$

    [  − 2 ,  2 ]

    $[0,\infty)$

  8. 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_plot8

    Image s20quiz01_pick_plot9

    Image s20quiz01_pick_plot10

    Image s20quiz01_pick_plot11

  9. Solve the equation $\displaystyle 4^{x}\,2^{x+1} = ( {{1}\over{2}}) 2^{2\,x}$

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

    $\displaystyle \left[ x=-{{1}\over{6}} \right] $

    [ x = −2 ]

    [ x = 2 ]

  10. Find the equation for the parabola shown below.

    Image s20quiz01_pick_plot12

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

    $\displaystyle y=-{{x^2}\over{2}}+2\,x-{{3}\over{2}}$

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

    $\displaystyle y={{x^2}\over{2}}-2\,x+{{3}\over{2}}$


Department of Mathematics
Last modified: 2026-01-21