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.

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

  7. 13.

    A graph of parabolas that are periodic about the x-axis with asymptotes at x = 0 and x = 3 pi over 2. A downward opening parabola has a vertex at (pi over 2, negative 3).

  8. 15.            

    A calculator graph of curves that are periodic about the x-axis. One curve rises from x = pi over 4 with decreasing steepness, inflects on the x-axis, then rises and approaches x = pi over 2.

  9. 17.

    A calculator graph of parabolas that are periodic about the x-axis with asymptotes at x = pi over 2 and x = 3 pi over 2. A downward opening parabola has a vertex at (pi, negative 1).

  10. 19.

    A calculator graph of curves that are periodic about the x-axis. One curve rises from the y-axis with decreasing steepness, inflects, then rises and approaches x = pi.

  11. 21.

    A calculator graph of parabolas that are periodic about the x-axis with asymptotes at x = pi over 4 and x = pi over 2. An upward opening parabola has a vertex at (pi over 8, 20). All data are approximate.

  12. 23.

    A calculator graph of curves that are periodic about the x-axis. One curve rises from x = 4 with decreasing steepness, inflects, then rises and approaches x = 10. All data are approximate.

  13. 25.

    1. tan x approaches ∞

    2. tan x approaches  − ∞

  14. 27. y =  − 3 sec(x / 2)

  15. 29.

    A graph of a curve that falls from the vertical x-axis with decreasing steepness to (1.57, 0).

  16. 31.

    A graph of an upward opening parabola with a vertex at (pi over 2, 2.83).
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