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The graph of the rational function

 

y = (ax - b)/(-2x + c)

 

is as shown below.  If x_1 = 5 and y_1 = 4, then what is a + b + c?

 

 May 3, 2020
 #1
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We have a vertical asymptote  at  x  = 5

 

This  means  that  -2(5)  + c  = 0      so   c = 10

 

Since we  have   a horizontal asymptote at  y  =4.....this means that  (a/-2)  = 4   so  a = -8

 

Also....it appears that the  point  (0,0)  is  on the graph

 

So    -8(0)  + b =  0     means that  b  = 0

 

So

 

a + b +  c   =  -8 + 0 + 10   =    2

 

 

cool cool cool

 May 3, 2020

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