Generating...                               s20quiz01_n5

  1. Sketch the graph of $\displaystyle -x^2-4\,x$.

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  2. Sketch the graph of $\displaystyle y={{1}\over{3^{\left\vert x\right\vert }}}$

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  3. Solve the equation $\displaystyle 5^{x-4}=25$

    [ x = 15625 ]

    [ x = −2 ]

    [ x = 29 ]

    [ x = 6 ]

  4. Find the vertex of $\displaystyle 2\,x^2-8\,x+12$.

    [  − 2 ,  4 ]

    [  − 4 ,  8 ]

    [ 2 ,  4 ]

    [ 4 ,  8 ]

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

    $[0,\infty)$

    [  − 2 ,  2 ]

    $(-\infty,\infty)$

    $[$ −2 $,\infty)$

  6. 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 = −2 ,  x =  − 1 ]

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

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

  7. Solve the equation $\displaystyle 3^{x-1}\,9^{x} = ( 27) 3^{5\,x}$

    [ x = −2 ]

    [ x = −14 ]

    $\displaystyle \left[ x={{28}\over{5}} \right] $

    [ x = −4 ]

  8. If a linear function $f$ satisfies f(4) = 3 and f(6) = 8, find $f(x)$.

    $\displaystyle y={{5\,x}\over{2}}+7$

    $\displaystyle y={{3\,x}\over{4}}-{{7}\over{2}}$

    $\displaystyle y={{5\,x}\over{2}}-7$

    $\displaystyle y={{3\,x}\over{4}}+{{7}\over{2}}$

  9. Sketch the graph of $\displaystyle y=\sqrt{x-3}+4$ .

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

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Department of Mathematics
Last modified: 2025-06-19