Joshua F.

asked • 09/03/23

Need help with finding a function

I'm trying to find a function with a Horizontal asymptote of -6, Vertical asymptotes of -1 and 3. It is supposed to have x intercepts of (-3,0) and (1,0). When I was using the asymptotes to find the equation I got (-6x^2)/(x^2-2x-3) but those don't appear to solve it.

Doug C.

Hi Joshua, Check out this graph to see if it helps you understand. desmos.com/calculator/r095wqts57 Post a reply here if you still need some help.
Report

09/03/23

Doug C.

Here is another graph with the horizontal asymptote included. desmos.com/calculator/wjsfevn25w
Report

09/03/23

2 Answers By Expert Tutors

By:

Hediye G. answered • 09/03/23

Tutor
5.0 (1,396)

Unlock Your Math Potential with Dr. Hediye's Expert Tutoring!
About this tutor ›
About this tutor ›

The vertical asymptotes tell you that the denominator is (x+1)(x-3)=x^2-2x-3 and you are right.

x intercepts tell you that the numerator is c(x+3)(x-1)= cx^2+2cx-3c where c is a constant.


So far we have f(x)=(cx^2+2cx-3c)/ (x^2-2x-3)


Horizontal asymptote tells you that the leading terms of numerator divided by the denominator is 6. That is (cx^2)/(x^2)=c=6


Therefore: f(x)=(6x^2+12x-18)/ (x^2-2x-3)


Upvote • 1 Downvote
More
Report

Josh F.

tutor
Yes to all except probably Hediye means c = -6, the given y-value of the horizontal asymptote. Btw, it is instructive to leave both numerator and denominator in factored form, as we can then see by inspection how the given information allows us to write the equation of the rational function: f(x) = [-6(x - 1)(x + 3)] / [(x - 3)(x + 1)] The zeros of the numerator generate the x-intercepts of the graph. The zeros of the denominator generate vertical asymptotes. A rational function will have a horizontal denominator different from the x-axis only when the degrees of the numerator and denominator are = , in which case the horizontal asymptote occurs at y = the ratio of the lead coefficients of the numerator and denominator (in this case -6 and 1). From one Joshua F. to another : )
Report

09/04/23

Hediye G.

tutor
Yes you are right, it should be -6. I remembered HA as 6 and the answer reflects that. Thank you Joshua.
Report

09/04/23

James S.

tutor
It might be worthwhile to give a brief explanation of BOBO, BOTN, and EATSDC here.
Report

09/06/23

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.