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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 21, 2020
 #1
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We have a "zero"   at x  = 4

 

This means that , in the numerator,   4  + A    =   0

So A =  -4

 

Also....we have a horizontal asymptote  at   y =  -1

Looking at the  coefficients on the  x variables in the numerator and denominato, taking their ratio  and setting it equal to this asymptote, we have that

1 / B =  -1

So   B   = -1

 

And we have a vertical asymprore at  x  = 3

This means  that, in the denominator,  -1 (3)  + C  = 0  →   C = 3

 

A + B + C =   

 

-4 -  1  +  3   =

 

-2

 

See the graph here to  confirm this  : https://www.desmos.com/calculator/tx6zbax7ra

 

 

cool cool cool

 Nov 21, 2020

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