Question

Describe the vertical asymptote(s) and hole(s) for the graph of y= (x+3)(x+4) / (x+4)(x+2).
Answers:
a) asymptote: x=3 and hole: x=-2
b) asymptote: x=-2 and hole: x= -4
c) asymptote: x=-2 and hole: x=4
d) asymptote: x=2 and hole: x=4

Answer 1

@nincompoop @Hero please help me

Answer 2

cross off what you Dont think is the answer

Answer 3

I WILL FAN + MEDAL PLEASE HELP !

Answer 4

@dumbcow @hick4life

Answer 5

for \(\color{green}{\rm Vertical~ asy.}\)
set the denominator equal to zero and then solve for the variable.
for\(\color{green}{\rm Horizontal ~asy.}\)
focus on highest degrees
~if the highest degree of the numerator is greater than the denominator then `No horizontal asy.` \[\color{reD}{\rm N}>\color{blue}{\rm D}\] example
\[\large\rm \frac{ 7x^\color{ReD}{3} +1}{ 4x^\color{blue}{2}+3 }\]
~if the highest degree of the denominator is greater than the highest degree of the numerator then `y=0` would be horizontal asy.
\[\rm \color{reD}{N}<\color{blue}{\rm D}\]
example:\[\large\rm \frac{ 7x^\color{red}{2}+1 }{ 4x^\color{blue}{3}+3 }\]
~if both degrees are the same then divide the leading coefficient of the numerator by the leading coefficient of the denominator
\[\rm \color{red}{N}=\color{blue}{D}\]
\[\large\rm \frac{ 8x^\color{reD}{3}+1 }{ 4x^\color{blue}{3}+3 }\] \[\rm \frac{ 8x^3 }{ 4x^3 } =2\] horizontal asy. =2

Answer 6

ok lets see what we got here

Answer 7

i will medal and fan if you get me the answer @hick4life

Answer 8

\[\rm f(x)=\frac{ (x+3)(x+4)}{ (x+2)(x+4)}\]
first simplify
is there anything you can cacnel out?

Answer 9

cancel*

Answer 10

Do we have a graph line

Answer 11

@jordanaz26 , just getting the answer wont help you on the next question...

Answer 12

yeah we can cancel out (x+4) @Nnesha

Answer 13

yes right!
so \[f(x)=\frac{ (x+3) }{ x+2}\]set the denominator equal to zero to find vertical asy

Answer 14

x+2=0
solve for x

Answer 15

Go ahead and cancel (4x+)

Answer 16

x=-2 @Nnesha

Answer 17

:=) looks good
wait a sec plz

Answer 18

sure ! so we got the vertical asymptote which is x:-2, but it also asks for the hole(s) @Nnesha

Answer 19

Its going to be B.

Answer 20

yeah i'mm trying to find hole in my notebook
i forgot how to find it

Answer 21

ahh okay
what are the factors that in common to both numerator and denominator ?

Answer 22

of 3 and 2 ? @Nnesha

Answer 23

common factors would be hole \[\rm f(x)=\frac{ (x+3)\color{reD}{(x+4)}}{ (x+2)\color{red}{(x+4)}}\]
in this question x+4 is common right
so set it equal to zero
x+4=0 solve for x that value would be hole

Answer 24

oh !!! so its x=-4 ! thank you so much ! fan and medal ! @Nnesha

Answer 25

my pleasure

Answer 26

and yes it's -4