Generating...                               s20quiz01_n16

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

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

    [ x = 1 ]

    $\displaystyle \left[ x={{1}\over{\ln 7+\ln 2}} \right] $

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

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

  3. Let $f(x) = 9-x^2$ , and let $g(x) = \sqrt{x}$ . Find the domain of  ${f\circ g}$.

    $[0,\infty)$

    $(-\infty,\infty)$

    $[$ −3 $,\infty)$

    [  − 3 ,  3 ]

  4. Sketch the graph for

    $\displaystyle f(x) = \begin{cases} -x & \mbox{if $x < 1$} \\ x-2 & \mbox{if $ 1 \le x \le 6$} \\ 1-x & \mbox{if $ 6 < x$} \end{cases} $

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  5. Sketch the graph for

    $\displaystyle f(x) = \begin{cases} x-1 & \mbox{if $x < 1$} \\ -x^2 & \mbox{if $ 1 \le x \le 4$} \\ 3-x & \mbox{if $ 4 < x$} \end{cases} $

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  6. Let $f(x) = \sqrt{x}-1$ , and let $g(x) = 25-x^2$ . Sketch the graph of  ${f\circ g}$.

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

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

    [  − 4 ,  8 ]

    [ 2 ,  4 ]

    [  − 2 ,  4 ]

    [ 4 ,  8 ]

  9. Find the equation for the parabola shown below.

    Image s20quiz01_pick_plot20

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

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

    $\displaystyle y=-{{x^2}\over{2}}+x+4$

    $\displaystyle y={{x^2}\over{2}}-x-4$

  10. Solve the equation $\displaystyle 2\,x^2-4\,x+1=0$.

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

    $\displaystyle \left[ x=-{{\sqrt{6}-2}\over{2}} , x={{\sqrt{6}+2}\over{2}} \right] $

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

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


Department of Mathematics
Last modified: 2026-03-24