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Unformatted text preview: g the formula f (x) = 4 − x2 .
Making a table as before, we see that as the x values sneak up to x = 1 in this fashion, the f (x)
values inch closer and closer1 to 4 − 12 = 3. To indicate this graphically, we use an open circle at
the point (1, 3). Putting all of this information together and plotting additional points, we get
0.999 f (x)
(x, f (x))
≈ 3.002 (0.999, 3.002) 2
−3 −2 −1
−4 1 We’ve just stepped into Calculus here! 1 2 3 x 66 Relations and Functions In the previous two examples, the x-coordinates of the x-intercepts of the graph of y = f (x) were
found by solving f (x) = 0. For this reason, they are called the zeros of f .
Definition 1.7. The zeros of a function f are the solutions to the equation f (x) = 0. In other
words, x is a zero of f if and only if (x, 0) is an x-intercept of the graph of y = f (x).
Of the three symmetries discussed in Section 1.3, only two are of signiﬁcance to functions: symmetry
about the y -axis and symmetry about the origin.2 Recall that we can...
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