Exercises 10.4, page 312

  1. 1. y = 5 cot 2x

    A calculator graph of curves that are periodic about the x-axis. One curve falls from the y-axis with decreasing steepness, inflects on the x-axis, then falls with increasing steepness toward approximately x = 1.6.

  2. 3. Undef.,  − 1.7 ,   − 1 ,   − 0.58 ,  0, 0.58, 1, 1.7, undef.,  − 1.7 ,   − 1 ,   − 0.58,0

    A graph of curves that are periodic about the x-axis. One curve rises from x = pi over 2 with decreasing steepness, inflects at (0, 0), then approaches x = pi over 2.

  3. 5. Undef., 2, 1.4, 1.2, 1, 1.2, 1.4, 2, undef.,  − 2 ,   − 1.4 ,   − 1.2 ,   − 1

    A graph of parabolas that are periodic about the x-axis with asymptotes at x = negative pi over 2 and x = pi over 2. An upward opening parabola has a vertex at (0, 1).

  4. 7.

    A graph of curves that are periodic about the x-axis. One curve rises from x = negative pi over 2 with decreasing steepness, inflects at (0, 0), then rises and approaches x = pi over 2.

  5. 9.

    A graph of parabolas that are periodic about the x-axis with asymptotes at x = negative pi over 2 and x = pi over 2. An upward opening parabola has a vertex at (0, one-fourth).

  6. 11.

  7. 13.

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