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Quiz 3

Mathematics Department
Tennessee Technological University


Date: December 13, 2018


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

    $ [0,\infty)$

    $ (-\infty,\infty)$

    [  − 5 ,  5 ]

    $ [$ −5 $ ,\infty)$

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

    \includegraphics{thisquiz_pick_plot0.ps}

    \includegraphics{thisquiz_pick_plot1.ps}

    \includegraphics{thisquiz_pick_plot2.ps}

    \includegraphics{thisquiz_pick_plot3.ps}

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

    \includegraphics{thisquiz_pick_plot4.ps}

    \includegraphics{thisquiz_pick_plot5.ps}

    \includegraphics{thisquiz_pick_plot6.ps}

    \includegraphics{thisquiz_pick_plot7.ps}

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

    \includegraphics{thisquiz_pick_plot8.ps}

    \includegraphics{thisquiz_pick_plot9.ps}

    \includegraphics{thisquiz_pick_plot10.ps}

    \includegraphics{thisquiz_pick_plot11.ps}

  5. Sketch the graph for

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

    \includegraphics{thisquiz_pick_plot12.ps}

    \includegraphics{thisquiz_pick_plot13.ps}

    \includegraphics{thisquiz_pick_plot14.ps}

    \includegraphics{thisquiz_pick_plot15.ps}

  6. Sketch the graph for

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

    \includegraphics{thisquiz_pick_plot16.ps}

    \includegraphics{thisquiz_pick_plot17.ps}

    \includegraphics{thisquiz_pick_plot18.ps}

    \includegraphics{thisquiz_pick_plot19.ps}

  7. Let $ f(x) = x^2-2\,x+3$ , $ x \ge 1$ . Find the inverse function $ f^{-1}$ .

    $ \displaystyle \sqrt{x-2}-1$ , $ x \ge$ 2

    $ \displaystyle \sqrt{x+2}+1$ , $ x \ge$ −2

    $ \displaystyle \sqrt{x-2}+1$ , $ x \ge$ 2

    $ \displaystyle \sqrt{x-1}+2$ , $ x \ge$ 1





Department of Mathematics
Last modified: 2018-12-13