Graphs, Or, the Graphical Representation of Algebraic Functions
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Graphs, Or, the Graphical Representation of Algebraic Functions

Graphs, Or, the Graphical Representation of Algebraic Functions


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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 Excerpt: ...? as A vty? large positive quantity. This gives us a point very near to-PB lot ith'ove It, ind at a very great distance to the right of YY Tnus'wh'en y" p'aJSes through the value--3, x changes abruptly from--oo to + oo. 54. From the above we see that y (ax--b) I (cx+d), where a, b, c, d stand for numbers, is the general type of such equations as that considered in the last paragraph, and that its graph will have two infinite branches with a pair of asymptotes parallel to the axes. Exercises. Draw the graphs of 10. y = x/(x-2). 11. y = (4+3)/(fi-6). 12. Find the equations of the asymptotes of y = (ax +6)/ (cx + d), and also the coordinates of the points in which it meets OX and OY. 55. Hyperbolas symmetrical with regard to both axes. Example.--Draw the graph of 4z2--9y2 = 36. Write this in the forms y = V42-36 (1) and x = + J V9y2 + 36 (2) It will be seen from (1) that x cannot be numerically less than 3, but there is no limit to the extent to which it may increase in magnitude; in fact x may increase numerically from +3 to + oo, and y from 0 to + oo. We shall attack this by plotting a few points for small values of x and y, and shall then indicate the form of the curve at an infinite distance. We get the same values of y when x is--3, --4, ... Plot these points, and then draw the straight lines whose joint equation is ix2--9y2 = 0, i.e. the lines 2x+Sy = 0 and 2x--3y. Let these be AOB, COD in figure. On examining the diagram we see that the graph consists of two branches, one in AOD, the other in BOC, and that the curve appears to approach nearer and nearer to the lines AOB, COD. We shall now show that as x increases indefinitely, the distance between the curve and AOB or COD becomes indefinitely small, in other words, AOB, COD are the asymptotes ...


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Product Details
  • ISBN-13: 9781236447012
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 36
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1236447018
  • Publisher Date: 22 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 82 gr


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