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The equation y = (x + A)/(Bx + C), where A,B, and C are integers, is shown below. What is A + B + C?

 

 Jun 3, 2021
 #1
avatar+121054 
+1

Step  by Step

 

The    horizontal  asymptote   =    -1

 

So     the  ratio  of coefficients on x  in the  numerator and denominator  =  1/B  = - 1

So  B  =  -1

 

The  vertical  asymptote    is   3

 

So....since this  value of  x  males the denominator =  0.....we  can solve  this

 

Bx +  C   =  0

-1x + C    =  0

-1 (3) + C  = 0

C   =  3

 

And  we  have   an  x  intercept    at  4

So

x  +  A  =  0

4  + A   =  0

A  =  -4

 

Here's  the  graph  :  https://www.desmos.com/calculator/zdco26ojf4

 

So

 

A  +  B   +  C    =

 

-4   + -1  +   3    =

 

-2

 

 

cool cool cool

 Jun 3, 2021

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