Real Mathematics Intended Mainly for Practical Engineers As An Aid to the Stud
Real Mathematics Intended Mainly for Practical Engineers As An Aid to the Stud
Ernest G Ernest George Beck
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The introduction of the term ( - 4a:) has had the effect of moving the axis of the curve 2 to the right of the origin ; and, again imagining the graph-templet as sliding in the circumferential groove of a tiny wheel at the lower extremity of the sling (or suspender), the point on the graph in con- tact with the wheel in the new position i. E. The right-hand graph in Fig. 61 ^will be that which formerly corresponded with x= -2, its ordinate being -7. This point, then EQUATIONS AND THEIR GRAPHS 2...03 and with it the whole graph ^has fallen through a distance equal to 11-7=4, which is reaUy 4" -f4 x 1. As a highly instructive exercise, the student is advised to draw and analyse the graphs corresponding to several sets of similar relations, such as 2/ = Sa;^ + 7a; - 2, and y = Sx^-5x + 4:; comparing them, on the lines indicated above, with a central graph representing y = 3x^. We may here anticipate later work slightly to observe that, given the relation y=ax^ + bx + c, the differential coefficient (that is, the rate of variation) of y with respect to x is | = 2x + 6.
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