The graph of the rational function
$y=\frac{ax-b}{-2x+c}$
is as shown above. If $x_1=5$ and $y_1=4$, what is the value of a+b+c ?
+128407 We have a horizontal asymptote at y = 4
This means that the ratio of the coefficients on x^2 in the numerator and denominator = 4
So
a/-2 = 4 ⇒ a = -8
And since we have a vertical asymptote at x = 5 , then
-2(5) + c = 0
c = 10
And (0,0) is on the graph which means that
2(0) - b = 0
So b = 0
So
a + b + c = -8 + 0 + 10 = 2
Here's a graph : https://www.desmos.com/calculator/fnsrqu4ihg
