How many vertical asymptotes does the function f(x)=ln(|(x+1)/(x^2-7x+12)| have?

Question

campbell_st · Answer

let the denominator equal zero, then solve for x

$$x^2 - 7x + 12 = 0$$

this can be done by factorising

the solutions will be the vertical asymptotes

poofypenguin · Answer

Alright...I understand that vertical asymptotes come from factoring the denominator, but the thing that's confusing me is that my solution manual says that the numerator will also cause a vertical asymptote... is that possible? Could you explain that to me, please?

anonymous · Answer

Numerator equaling 0 would cause a horizontal asymptote I believe.

poofypenguin · Answer

Are you sure? Cuz both my prof and my answer key says that it'll be a vertical asymptote...I'm so confused right now...:/

campbell_st · Answer

the numerator may cause a point of discontinuity.. 

e.g. 

$$\frac{(x + 1)}{(x + 1)(x + 5)}$$

(x + 1) is a common factor... so the curve is discontinuous at that point. 


a horizontal asymptote may come form the numerator... and is easily found by division.

campbell_st · Answer

oops I missed that it was a log function 

and with a log function you can also get a asymptote from the numerator... 

x = -1

they are the values tha make it undefined... x = 3, and x = 4

and given its a log function... you can't find the log of zero. 

so the numerator can't be zero 

so solve x + 1 = 0 to find the asymptote. 

x = -1

so x can't be -1

hope that helps

tkhunny · Answer

It's a logarithm!  What happens when the argument of the logarithm is zero (0)?

campbell_st · Answer

hope that makes some sense

poofypenguin · Answer

Yes! I get it now! Thanks so much! :D