Barrons AP Calculus

(a)

(a)

(b)

Figure  N4–8

Verify the preceding on your calculator, using [–4,4] × [–4,8].

Example 20 __

Describe any symmetries of the graphs of

3 y     2    + x    =   2;  (b) y   =   x   +    ;  (c) x^2     −   3y  2   =   27.

SOLUTIONS:

Suppose point   (x, y)  is  on  this    graph.  Then    so  is  point   (x, −y),    since   3(−y)^2 +

x   =   2   is  equivalent  to  3y  2    + x    =   2.  Then    (a) is  symmetric   about   the x-axis.

Note    that    point   (–x,    –y) satisfies   the equation    if  point   (x, y)  does:.

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