## anonymous one year ago 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

1. anonymous

2. Hayleymeyer

cross off what you Dont think is the answer

3. anonymous

4. anonymous

@dumbcow @hick4life

5. Nnesha

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

6. hick4life

ok lets see what we got here

7. anonymous

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

8. Nnesha

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

9. Nnesha

cancel*

10. hick4life

Do we have a graph line

11. dumbcow

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

12. anonymous

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

13. Nnesha

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

14. Nnesha

x+2=0 solve for x

15. hick4life

Go ahead and cancel (4x+)

16. anonymous

x=-2 @Nnesha

17. Nnesha

:=) looks good wait a sec plz

18. anonymous

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

19. hick4life

Its going to be B.

20. Nnesha

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

21. Nnesha

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

22. anonymous

of 3 and 2 ? @Nnesha

23. Nnesha

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

24. anonymous

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

25. Nnesha

my pleasure

26. Nnesha

and yes it's -4