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The graph of the rational function

$y=\frac{ax-b}{-2x+c}$

is as shown above. If $x_1=5$ and $y_1=4$, what is the value of a+b+c ?

 

 Dec 27, 2020
 #1
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We  have a horizontal asymptote at y  = 4

 

This means  that  the ratio of the coefficients on  x^2  in the  numerator and denominator =   4

 

So

 

a/-2   = 4    ⇒    a   =   -8

 

And since we have a vertical asymptote  at   x  = 5 , then

 

-2(5) + c   =  0

c = 10

 

And (0,0)  is on the  graph  which means that

 

2(0)  - b   =  0

So b = 0

 

So

 

a + b + c  =  -8  + 0  +  10    = 2

 

Here's a graph :  https://www.desmos.com/calculator/fnsrqu4ihg

 

 

cool cool cool

 Dec 27, 2020

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