Question

F the graph of y=ax+b/x+c has a horizontal asymptote y=2 and a vertical asymptote x=-3 then a+c=?

Answer 1

Correct answer is E.

$y= \frac{ax+b}{x+c} \\ \\ \lim_{x \to \infty} \frac{ax+b}{x+c}=2 \\ \\ \lim_{x \to \infty} \frac{ \frac{ax}{x} + \frac{b}{x} }{ \frac{x}{x} + \frac{c}{x} }=2 \\ \\ \lim_{x \to \infty} \frac{a + \frac{b}{x} }{ 1 + \frac{c}{x} }=2 \\ \frac{a + 0}{ 1 + 0 }=2 \\ \\ \frac{a}{1} =2 \\a=2 \\ \\x+c=0 \\-3+c=0 \\c=3 \\ \\a+c=2+3=5$