Stitz-Zeager_College_Algebra_e-book

A clue as to how to proceed is in the numerators in

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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 y 4 3 x 0.9 0.99 0.999 f (x) (x, f (x)) 3.19 (0.9, 3.19) ≈ 3.02 (0.99, 3.02) ≈ 3.002 (0.999, 3.002) 2 1 −3 −2 −1 −1 −2 −3 −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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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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