For the webwork you will need to know the following:

(1) To test for symmetry about the y-axis:

  Replace x with (-x).
  If you get an equivalent equation
  then the graph is symmetric about the y-axis.

(2) To test for symmetry about the x-axis:

  Replace y with (-y).
  If you get an equivalent equation
  then the graph is symmetric about the x-axis.

(3) To test for symmetry about the x-axis:

  Replace x with (-x) and replace y with (-y).
  If you get an equivalent equation
  then the graph is symmetric about the origin.

Important points:

(A) When you substitute, to be safe you must use parentheses.

  example: the equation y = x^2 has symmetry about the y-axis
    because when you replace x with (-x) you get the same equation.

(B) Symmetry means that you get an equivalent equation,
    not that you get the same equation.

  example: the equation y = x^3 has symmetry about the origin
    because when you replace y with (-y) and x with (-x) you
    get the equation -y = -x^3 which is equivalent to
    the equation y = x^3.

(C) To prove that a symmetry does NOT exist you only
    need to find one point on the graph for which the
    reflection is not on the graph.  (But to prove that
    symmetry does exist it is not enough to consider
    individual points.)

  example 1: y = x^3 is NOT symmetric about the y-axis
    because the point (1,1) is on the graph but
    the point (-1,1) is not.
  (example 2: The points (1,0) and (-1,0) are both on
    the graph of y=x(1-x^2), but the graph is not even.)

Two hints about inequalities that could help you with
the webwork:

(1) interval notation (important for webwork)

  The inequality
  
    x<7

  says that x is strictly between -infinity and 7.
  So x lies in the interval

    (-infinity,7)

  which is what you would enter in webwork.

  The inequality

    1 < x ≤ 7

  Says that x is strictly greater than 1
  and less than or equal to 7.  So x lies in the interval

    (1,7]

  which is what you would enter in webwork.

(2) You solve inequalities much like equations
  with one very important difference: When you multiply or
  divide both sides of an equation by a number, if the number is
  negative then the inequality is *reversed*.

  So to solve

    1 ≤ 3-2x < 7

  (which actually stands for two inequalities

    1 ≤ 3-2x   and  3-2x < 7)

  you first subtract 3 to get

    -2 ≤ -2x < 4

  and then divide by -2 to get

    1 ≥ x > -2

  So the solution is the interval  (-2, 1].