Generating...                               s20quiz01_n10

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

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  2. Find the equation for the parabola shown below.

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

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

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

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

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

    $\displaystyle \left[ x={{\ln 3}\over{\ln 4+\ln 3}} \right] $

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

    [ x = 1 ]

    $\displaystyle \left[ x={{1}\over{\ln 4+\ln 3}} \right] $

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

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

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

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

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

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

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

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

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

    [ x = 0 ,  x = 5 ]

  6. If a linear function $f$ satisfies f( − 2) = −3 and f(0) = −5, find $f(x)$.

    y = −x − 5

    $\displaystyle y={{3\,x}\over{2}}+5$

    $\displaystyle y={{3\,x}\over{2}}-5$

    y = 5 − x

  7. Sketch the graph for

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

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  8. Solve the equation $\displaystyle 2^{x-2}\,8^{x} = ( 4) 2^{2\,x}$

    [ x = 2 ]

    $\displaystyle \left[ x={{6}\over{7}} \right] $

    [ x = −4 ]

    [ x = 3 ]

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

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

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

    [ x = 2 ]

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

    [ x = 0 ]


Department of Mathematics
Last modified: 2025-05-04