What does the graph of lnx^2 look like?

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Discussion Overview

The discussion revolves around understanding the graph of the function \( \ln x^2 \). Participants explore the nature of the function, its properties, and the challenges associated with graphing it.

Discussion Character

  • Conceptual clarification
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant asks what the graph of \( \ln x^2 \) looks like.
  • Another participant seeks clarification on whether the expression is \( \ln x^{2} \) or \( (\ln x)^{2} \), suggesting that the original poster should graph it themselves.
  • A participant confirms it is \( \ln x^2 \) and expresses difficulty in graphing it despite having calculated various properties such as domain and asymptotes.
  • One participant suggests that knowing the graph of \( \ln x \) can help in graphing \( \ln x^2 \), noting that \( \ln x^2 = 2\ln x \).
  • Another participant relates \( \ln x \) to the graph of \( e^x \) by mentioning their inverse relationship.
  • A participant questions if \( \ln x^2 \) is simply \( \ln x \) stretched by a factor of 2.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the graphing process, and there are varying levels of understanding regarding the properties of \( \ln x \) and its transformations.

Contextual Notes

Some participants express uncertainty about their graphing abilities and the relationship between \( \ln x \) and \( \ln x^2 \), indicating a need for further clarification on these concepts.

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what does the graph of lnx^2 look like?
 
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Is that [tex]\ln x^{2}[/tex] ot [tex](\ln x)^{2}[/tex] ??If so,why don't u graph it??Do u know how??

Daniel.
 
it is lnx^2 (the first one) and i can't graph it. i don't know how. I've found all of the info ex. domain, asymptotes,intervals of increase/decrease, local min/max, concavity, and Inflection points

i can do those steps but have difficulty graphing functions

(and no graphing calc to check solutions)
 
If you know what [itex]\ln x[/itex] looks like, you can easily graph [itex]\ln x^2[/itex], since [itex]\ln x^2=2\ln x[/itex].

If you don't know what [itex]\ln x[/itex] looks like, it's the graph of [itex]e^x[/itex] when mirrored through the line y=x, because they are the inverse functions of each other.

If you don't know what [itex]e^x[/itex] looks like..., well you should.
 
i do...but is it lnx just stretched by 2?
 
thankx you!
 

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