About the Book
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 edition. Excerpt: ...temperature increase most rapidly? 299. Graph of a function. To represent the various values which an algebraic function, e.g. 3 + x--x2, assumes, when x changes from--3 to + 9, let us substitute in 3 + f x--% x2, successively the values--3, --2, --1, 0, 1, etc. If x respectively =-3, -2, -1, 0,1, 2,3, 4,5, 6,7, 8, 9, then 3 + x-ia;2 =-3, -1, 1J, 3, 4J, 5, 5J, 5, 4J, 3, 1J, -1, -3f.' Selecting any convenient length as a unit, we lay off on a line OX from O the values of x, and at each point erect a perpendicular equal to the corresponding value of To find e.g. the point representing that, for x = 2, 3 + f x-x2 = 5, we lay off OA = 2, and at A draw a perpendicular AB=5. Similarly for all other points, as C, D, etc. Since the positive values of x are laid off from 0 toward X, negative values of x must be laid off from 0 in the opposite direction; as OF=--2. Similarly negative values of 3 + f a;--x2 must be laid off in a direction opposite to the positive values, as FO =--1, or m =-3f. 300. The lines OA and AB are called the coordinates of point B, OA is the abscissa, AB the ordinate of point B. The abscissa of I is OH, its ordinate HI.. 301. The line OX is called the axis of abscissas or jr-axis. The perpendicular OY, erected at O, is the axis of ordinates or/-axis. The point 0 is called the origin. Abscissas measured to the right of the origin, and ordinates above the a;-axis, are considered positive. 302. The point whose abscissa is x and whose ordinate is y is often represented by (x, y). Thus (2, 5) represents the point B, (-2, -1) is the point O. The point (x, y) can also be obtained by first laying off y on the y-axis, and then drawing x perpendicular to oy at the extremity of y. 303. If we should represent the values of the function 3 + f..
