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Quiz 2

Mathematics Department
Tennessee Technological University


Date: December 13, 2018


  1. Find the vertical asymptotes for $ \displaystyle {{-3\,x-2}\over{x^2-6\,x-7}}$.

    [ x = −6 ,  x =  − 7 ]

    [ x = 1 ,  x = −7 ]

    [ x = −1 ,  x = 7 ]

    [ x = 6 ,  x = 7 ]

  2. Let $ \displaystyle y=-{{4\,x+23}\over{x^2+9\,x+14}}$ be a quotient function. Find the two reciprocal function $ \frac{a_1}{x + b_1}$ and $ \frac{a_2}{x + b_2}$ so that the function can be expressed as $ y = \frac{a_1}{x + b_1} + \frac{a_2}{x + b_2}$

    $ \displaystyle y={{1}\over{x+7}}-{{3}\over{x+2}}$

    $ \displaystyle y=-{{1}\over{x+7}}-{{3}\over{x+2}}$

    $ \displaystyle y=-{{3}\over{x-2}}-{{1}\over{x-7}}$

    $ \displaystyle y={{1}\over{x-7}}-{{3}\over{x-2}}$

  3. Sketch the graph of $ \displaystyle {{1-2\,x}\over{4\,x-7}}$.

    \includegraphics{thisquiz_pick_plot0.ps}

    \includegraphics{thisquiz_pick_plot1.ps}

    \includegraphics{thisquiz_pick_plot2.ps}

    \includegraphics{thisquiz_pick_plot3.ps}

  4. Express the quotient function $ \displaystyle y={{x+6}\over{x-1}}$ in the form of $ \displaystyle y={{a}\over{x-1}}+b$ . Find the values $ a$ and $ b$.

    $ \displaystyle y={{7}\over{x-1}}-1$

    $ \displaystyle y={{7}\over{x-1}}+1$

    $ \displaystyle y={{1}\over{x-1}}+7$

    $ \displaystyle y={{1}\over{x-1}}-7$





Department of Mathematics
Last modified: 2018-12-13