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

Ok sir, since the equation is...
ax+b÷x+c

x on the top is the same degree as it is on the bottom.
meaning, x is not raised to 2 or 3, but the x on both top and bottom are both raised to 1. (not shown, doesn't need to be shown) If both are raised to the same number, then you simply divide the coefficients of the x's (if no coefficient, then you regard it as a 1)
Since they stated that it is equal to 2. You can look at the denominator and see that there is no coefficient meaning it is 1. The only way it could be possible is if a=2. If you divide the coefficients you would get 2/1=2.
Now we established a=2. Now for c.
To get a vertical asymptote, the denominator must me equal to 0.
Set the denominator equal to 0 and it will look like:
x+c=0
If we were given that the asymptote is -3, then the number to make it 0 would be positive 3. So since x would be -3, c=3.

Now you add a+c and get 3+2 which is equal to 5.

Answer 2

can u explain the first two steps clearer.... not sure how u got 2/1

Answer 3

Umm,
All you need to focus on is ax/x
the answer is 2.
the coefficient is (a)/(1)
then you think, what over 1 is equal to 2...and its 2.

Answer 4

but why does it have to be 2? because of the horizontal asymptote?