Variable-only graphing question

[Emethyst]

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.

 

[HallsofIvy]

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.

 

[Emethyst]

Ahh I think I see now. I'm guessing by the laws of logarithms you mean simplify log(kx^n) to logk + nlogx?