Generating...                               s20quiz01_n7

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

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

    [ 3 ,   − 1 ]

    [ 3 ,  1 ]

    [  − 3 ,  1 ]

    [  − 3 ,   − 1 ]

  3. Sketch the graph of $\displaystyle 2\,x^2-12\,x+22$.

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

    [ x = 0 ,  x = 5 ]

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

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

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

  5. Let $f(x) = \left\vert x\right\vert $ , and let $g(x) = \sqrt{x+1}-3$ . Sketch the graph of  ${f\circ g}$.

    Image s20quiz01_pick_plot8

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  6. If a linear function $f$ satisfies f( − 2) = 5 and f( − 4) = 2, find $f(x)$.

    $\displaystyle y=-{{5\,x}\over{2}}-8$

    $\displaystyle y=8-{{5\,x}\over{2}}$

    $\displaystyle y={{3\,x}\over{2}}-8$

    $\displaystyle y={{3\,x}\over{2}}+8$

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

    Image s20quiz01_pick_plot12

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  8. Sketch the graph of $\displaystyle y=\sqrt{x-3}+2$ .

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  9. Solve the equation $\displaystyle 4^{x}=5^{2-x}$

    [ x = 1 ]

    $\displaystyle \left[ x={{2}\over{\ln 5+\ln 4}} \right] $

    $\displaystyle \left[ x={{2\,\ln 5}\over{\ln 5+\ln 4}} \right] $

    [ x = 2 ]

  10. Solve the equation $\displaystyle {{3^{x+1}}\over{9^{x}}} = ( {{1}\over{3}}) 3^{x}$

    [ x = 2 ]

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

    [ x = −6 ]

    [ x = 1 ]


Department of Mathematics
Last modified: 2026-09-10