Question

Describe the end behavior of the rational function g(x) = - (6x+1)/(x+2)

Answer 1

is this for calculus?

Answer 2

Algebra 2

Answer 3

With trig

Answer 4

do you know how to find horizontal asymptotes?

Answer 5

Doesn't it depend on the type of function it is??

Answer 6

y = (-6x-1)/(x+2) solve for x
y(x+2) = -6x-1
yx+2y = -6x-1
yx+6x=-1-2y
x(y+6)=-(1+2y)
x=-(1+2y)/(y+6)

Answer 7

I thought the horizontal asymptote for this one would be 6

Answer 8

the domain of this is the range of the starting function

Answer 9

yes

Answer 10

this is the end behavior

Answer 11

-6

Answer 12

y=-6 is the end behaivior

Answer 13

So the end behavior is the horizontal asymptote?

Answer 14

or, the opposite of?

Answer 15

as x approaches +-infinity, f(x) approaches -6

Answer 16

The highest powers determine end behaviour. Compare the highest powers of x in the numerator and denominator:

\[\Large g(x) = \frac{ -6x-1 }{ x+2 }\]
On the top, the highest power is the -6x. On the bottom, it's x.

Then you divide them like so \[\large y= \frac{ -6x }{ x } = -6\]

Answer 17

thank you guys