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=?

a)-3
b)-1
c)0
d)1
E)5 ...?

Answer 1

Answer: 5

Explanation:

Lim x-> a (ax+b)/x+c = a you know that a=2

Since the limit of x ->-3 equals infinity, you know that x =3.

Thus a+c = 5

Answer 2

Correct answer is E.


`y= (ax+b)/(x+c) \\ \\ \lim_(x \to \infty) (ax+b)/(x+c)=2 \\ \\ \lim_(x \to \infty) ( (ax)/(x) + (b)/(x) )/( (x)/(x) + (c)/(x) )=2 \\ \\ \lim_(x \to \infty) (a + (b)/(x) )/( 1 + (c)/(x) )=2 \\ (a + 0)/( 1 + 0 )=2 \\ \\ (a)/(1) =2 \\a=2 \\ \\x+c=0 \\-3+c=0 \\c=3 \\ \\a+c=2+3=5`