Finding Limits & Hor. Asymptotes of f(x) Using Graphs & Tables

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Homework Help Overview

The discussion revolves around finding limits and horizontal asymptotes for the function f(x) = (2x + 5) / |3x - 4| using graphical and tabular methods. Participants are exploring the behavior of the function as x approaches both positive and negative infinity.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to determine the limits at positive and negative infinity using a graphing calculator and a table of values. They question the correctness of their findings regarding horizontal asymptotes and seek clarification on their interpretation.

Discussion Status

Some participants have confirmed the use of a graphing calculator for this problem and have not introduced alternative methods like L'Hôpital's rule. There is an ongoing exploration of the limits and asymptotic behavior, with no explicit consensus reached on the horizontal asymptotes yet.

Contextual Notes

Participants note that the problem specifies using graphs and tables, and there is uncertainty regarding the necessity of finding vertical asymptotes.

Jacobpm64
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For f(x) = (2x + 5) / |3x - 4|, use graphs and tables to find the limit as x approaches infinity of f(x) and the limit as x approaches negative infinity of f(x)... Also identify any horizontal asymptotes...

When i graph the function in my graphing calculator, it looks like y will never reach a specific value as x approaches pos or neg infinity.. i went to table and checked at x value or 20000000 and -200000000 and i get 2/3 and -2/3 respectively

is this correct?
limit as x approaches pos inf = 2/3
limit as x approaches neg inf = -2/3

I'm not sure about the horizontal asymptotes?
would they be y = 2/3 and y = -2/3? I think? or is it something in between that?

Thanks for the input.
 
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Yes, are you supposed to find the answer with a graphing calculator or L'Hoptial's rule? Did you have to find the vertical asymptote?
 
i'm guessing a graphing calculator.. because it says graphs and tables.. we've never done L'Hopital's rule
 
Okay, then looks like you are golden.
 

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