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How do we know that the graph of y = x 2 doesn't look like one of these curves? (2.4) Plot the points (x,y) whose coordinates appear in the table, and draw a smooth curve (labeled with its equation) through the plotted points (see Figure 1.5).Solution Make a table ofxy-pairs that satisfy the equation y = x 2 then the value y = f(x) is the height of the graph above the poiut x (or below x if The height may be positive or negative, depending on the sign of j(x) (Figure 104).įIGURE 1.3 The graph of f(x) = x + 2 is the set of points (x,y) for whichy has the value x + 2.į. y) is a point on the graph, then y = j(x) is the height of the graph above the pointx. The graph of a function j is a useful picture of its behavior. Its graph is the straight line sketched in Figure 1.3. The graph of the function j(x) = x + 2 is the set of points with coordinates (x,y) for which y = x + 2. In set notation (see Appendix 1), the rangeis. The range of y = x 2, X ,: 2, is the set of all numbers obtained by squaring numbers greater than or equal to 2. The artist was not thinking of calculus when he composed the image, but rather, of a visual haiku consisting of a few elements that would spaIl 0." Changing the domain to which we apply a formula usually changes the range as well. tratioDl: Karen Heyt, lllustraThch Cover Design: Rokusck Design Cover image: Forest Edge, Hokuto, Hokkaido, Japsn 2004 © Michael Kenna About the cover: The cover image of a tree line on a snow-swept landscape, by the photographer Michael Kenna, was taken in Hokkaido, Japan.
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