Question

Find the horizontal or oblique asymptote of f(x) = 2x^2+5x+6/x+3
a. y = -3
b. y = 2x - 1
c. y = 5
d. y = -2x + 5
@satellite73 @jim_thompson5910 @Directrix @SolomonZelman @iambatman @Callisto @wio

Answer 1

divide

Answer 2

i dont know how

Answer 3

you get a quotient and a remainder
ignore the remainder, the quotient is your "oblique" asymptote

Answer 4

synthetic division is easiest in this case

Answer 5

how do i do that? can you show me?

Answer 6

but you can do long division too if you want

Answer 7

list the coefficients
they are

2 5 6

Answer 8

can you show me please how to?

Answer 9

then put a -3 on the side
2 5 6
-3
___________

Answer 10

bring down the 2
2 5 6
-3
___________
2

Answer 11

then \(-3\times 2=-6\) put it under the 5

2 5 6
-3 -6
___________
2

Answer 12

add and get \(5-6=-1\)

2 5 6
-3 -6
___________
2 -1

Answer 13

now you can continue to get the remainder, but you do not need the remainder only the quotient
you read off the coefficients from the bottom line

Answer 14

can you continue?
i dont know what to do after?

Answer 15

divide a polynomial of degree 2 by a polynomial of degree 1, get a polynomial of degree 1
so answer is \(2x-\)

Answer 16

oops \\[y=2x-1\] is what i meant to write

Answer 17

2 5 6
-3 -6
___________
2 -1
y = 2x -1