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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?

 

 Nov 29, 2020
 #1
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We have a horizontal asymptote at  y  = -1

 

This   means  that  the ratio of the  coefficients  on the  x variables  are

 

1 / B =  - 1   →   B   = -1

 

Since we  have an  x intercept at  4....this implies that   4 + A  =  0  →   A  = -4

 

And finally, since  we  have  a vertical asymptote at x  = 3, this means  that

 

-1(3)  +  C  =  0

 

C  =  3

 

So...our function is

 

x - 4

_____

-x + 3

 

A  + B + C = -4  -1  + 3   =  -2

 

cool cool cool

 Nov 29, 2020

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