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