+0

# Graphing question

0
106
1

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

May 19, 2022

#1
+9461
0

Note that when x = 4, y = 0. Then substituting (x, y) = (4, 0) gives:

$$\dfrac{4 + A}{4B + C} = 0\\ 4 + A = 0\\ A = -4$$

Now, note that the vertical asymptote occurs at x = 3. That means the denominator (Bx + C) is 0 when x = 3. Then 3B + C = 0.

Then, note that $$\displaystyle\lim_{x\to \infty} y = -1$$ since y approaches -1 when x approaches infinity. Then $$\dfrac1B = -1\implies B = -1$$.

Since 3B + C = 0, C = 3.

Therefore, the function is $$y = \dfrac{x - 4}{-x + 3}$$. A + B + C = -4 + (-1) + 3 = -2.

May 19, 2022