242 



NEW MODE OF REPRESENTING 



Y = f(x), when x <, a, and greater than o — 



Y = fi(^), when x > a 



Fig. 3. 



B H 



Let the discontinuous curves AC, CP, Fig. 3, 

 be produced, from the point of intersection C, to 

 the points D and D, respectively. Draw FPE, 

 GPiH perpendicular to AB — it will readily be 

 seen that, for every value of x on the axis AB, 

 there will be two values of the ordinate, viz. : 

 PE and FE ; except in the particular case when 

 X rr a. For when x :=: AE, we have the corre- 

 sponding ordinates EP and EF, the first of which 

 refers to the curve AC, whose equation \s 9/ — 

 f(x) and the second refers to the curve CPj whose 

 equation is2/—fi{x). If we take <r i=: AH we shall 

 have in the same manner two values of the ordi- 

 nate, viz. : GH and PiH. It appears from the 

 above considerations, that the value of Y must 

 partake of the .lature of a quadratic equation, or 



