Question

Man if you could help me out i'll plant a tree in your name.
what is the graph of the rational function (x+2)(x+4)/(x+4)(x+1)
looking for asymptotes and holes

Answer 1

What do you think?

Answer 2

Well if i knew what a hole was that would help haha

Answer 3

yeah would help

Answer 4

Symplifing se got
(x+2)/(x+1)
Obviusly x could not be -1 so here is a hole

Answer 5

Just to be clear: please type out the numerator of your rational fraction here.

Next, type out the denominator here.

Can this rational function be simplified by cancelling or reduction? Explain.

Answer 6

So you could cancel out the x+4's leaving x+2/x+1 correct?

Answer 7

Yes

Answer 8

So my confusion lies in why -1 would be a hole, but not -2. What is it i'm misunderstanding?

Answer 9

To find asymptotes just make a limit
Lim x-->0 (x+2)/(x+1) that give us 2

Answer 10

Because when you replace -1 in the function it give us 1/0 and this is imposible so the function is not continous in this point

Answer 11

ohh alright, thank you all for actually leading me to the answer instead of just giving it to me!

Answer 12

Ok No problem

Answer 13

the numerator's equation has a degree of 1
the denominator's equation has a degree of 1

the leading term coefficient for each is 1
\(\bf \cfrac{{\color{brown}{ 1}} x^{\color{blue}{ 1}}+2}{{\color{brown}{ 1}} x^{\color{blue}{ 1}}+1}\quad thus\implies \cfrac{{\color{brown}{ 1}}}{{\color{brown}{ 1}}}\iff 1\implies y=1\impliedby \textit{horizontal asymptote}\)