Find the horizontal asymptote of the rational function f(x)=8x-12 divided by 4x-2?

Answer 1

Let y = (8x - 12) / (4x - 2).

The vertical asymptote happens when the denominator is 0 (e.g. 4x - 2 = 0, 4x = 2, x = 1/2. But the question asked about the horizontal asymptote.

To solve this, solve the equation for x:
y = (8x - 12) / (4x - 2)

Multiply both sides by (4x - 2)
(4x - 2) y = 8x - 12

Distribute through:
4xy - 2y = 8x - 12

Now put x on one side:
4xy - 8x = 2y + 12

Distribute out 4x:
4x(y - 2) = 2(y + 6)

Divide both sides by (y-2):
4x = 2(y + 6) / (y - 2)

Divide both sides by 4:
x = 1/2 (y + 6) / (y - 2)

Now when will this have a numerator of zero? It is when y - 2 = 0
y - 2 = 0
y = 2

So the horizontal asymptote is y = 2.

Answer 2

the horizontal asymtote is equal to 2. The reason is because you look at the first two numbers. look at 8x and 4x. those are the only variables that matter. you say 8x divided by 4x, that equalss 2. Because the 8x and 4x has the same power so you say 8/4 which is 2. The horizontal asymtote is 2. if there is a power of 2 on top like 8x^2, then there is none. if there is a power or 2 on the bottom like 4x^2 the horizontaly asymtote is 1.

Answer 3

When the degree of the numerator = the degree of the denominator,
the horizontal asymptote is y = (leading coefficicient of numerator)/(leading coefficient of denominator)
= 8/4 = 2

Answer 4

First, you do this:
y=(8x-12)/4x-2

Multiply 4x-2 on both sides:
y(4x-2)=8x-12

Distributive Property:
4xy-2y=8x-12

Subtract 8x on both sides and add 2y on both sides:
4xy-8x=2y-12

Factor out 4x:
4x(y-2)=2y-12

Factor out the 2:
4x(y-2)=2(y-6)

Divide both sides by y-2:
4x=2(y-6)/(y-2)

Divide both sides by 4:
x=(1/2) (y-6)/(y-2)

Set y-2 to 0:
y-2=0
y=2

Horizontal asymptote:
y=2

Answer 5

for any horizontal asymtotes look for the highest power of X.

if its in the top of the equation, there is none.
if its in the bottom of the eqation, then its always y=0
if its the same in both, as it is in this quesiton, then its the coefficient of the top over the coefficient of the bottom.

here 8/4=y=2

Answer 6

f(x) = 4(2x - 3)/(2(2x - 1)
= 2 ((2x - 1) - 2)/(2x - 1)
= 2 (1 - 2/(2x - 1))
As x → ±∞ 2/(2x - 1) → 0 and f(x) → 2(1 - 0) ie 2

Thus the horizontal asymptote is y = 2