Unformatted text preview: or, if you can believe it! 1.3 Graphs of Equations 1.3.1 27 Exercises 1. For each equation given below
• Find the x- and y -intercept(s) of the graph, if any exist.
• Following the procedure in Example 1.3.2, create a table of sample points on the graph
of the equation.
• Plot the sample points and create a rough sketch of the graph of the equation.
• Test for symmetry. If the equation appears to fail any of the symmetry tests, ﬁnd a
point on the graph of the equation whose reﬂection fails to be on the graph as was done
at the end of Example 1.3.3
(a) y = x2 + 1
(b) y = x2 − 2x − 8 (c) y = x3 − x
(d) y =
(e) y = x3
√ − 3x x−2
(f) y = 2 x + 4 − 2 (g) 3x − y = 7
(h) 3x − 2y = 10
(i) (x + 2)2 + y 2 = 16
(j) x2 − y 2 = 1
(k) 4y 2 − 9x2 = 36
(l) x3 y = −4 2. The procedures which we have outlined in the Examples of this section and used in the exercises given above all rely on the fact that the equations were “well-behaved”. Not everything
in Mathematics is quite so tame, as the following equations will show you. Discuss with your
classmates how you might approach graphing these equations. What diﬃculties arise when
trying to apply the various tests and procedures given in this section? For more information,
including pictures of the curves, each curve name is a link to its page at www.wikipedia.org.
For a much longer list of fascinating curves, click...
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