Variable-only graphing question

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SUMMARY

The discussion centers on graphing the function F=Kx^n, where K>0 and n>1. Participants clarify that the graph of F vs. x is not linear but rather a curve that reflects the power relationship. The graph of F vs. x^n is confirmed to be a linear representation, while the log-log transformation logF vs. logx simplifies to logk + nlogx, revealing a linear relationship with slope n. This understanding is crucial for interpreting the behavior of power functions and their logarithmic forms.

PREREQUISITES
  • Understanding of power functions and their properties
  • Familiarity with logarithmic transformations
  • Basic graphing skills for polynomial functions
  • Knowledge of the laws of logarithms
NEXT STEPS
  • Study the characteristics of polynomial graphs, specifically F=Kx^n
  • Learn about logarithmic properties and their applications in graphing
  • Explore the implications of linear relationships in log-log graphs
  • Practice sketching various power functions and their transformations
USEFUL FOR

Students in mathematics or physics, educators teaching graphing techniques, and anyone interested in understanding the relationships between power functions and their logarithmic forms.

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Homework Statement


If F=Kx^n, where K>0 and n>1, sketch the graphs of F vs. x, F vs. x^n, and logF vs. logx. What information is obtained from each graph? Be specific.



Homework Equations


n/a



The Attempt at a Solution


No idea where to start with this one, as it's stumping me greatly. From the information given, I'm guessing that for the first graph of F vs. x it will be a simple linear graph, F vs. x^n will be a vertical parabola, and logF vs. logx will be a horizontal parabola, however, I'm unsure what information these graphs would give me (if they are even the right graphs I need to draw). If someone could point me in the right direction here it would be greatly appreciated, thanks in advance.
 
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Why would you guess "that for the first graph of F vs. x it will be a simple linear graph"? What you normally see are graphs of "F vs. x". What does the graph of F= 2x^2 look. Now suppose you replace x^2 by u to get F= 2u. What would a graph of F= 2u look like? Finally, there is no need to guess about the third question, go ahead and take the logarithms. log(F)= log(kx^n)= ? Use the laws of logarithms.
 
Ahh I think I see now. I'm guessing by the laws of logarithms you mean simplify log(kx^n) to logk + nlogx?
 

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