Hi,

I was wondering how increasing the power of an equation would transform a graph?

e.g

y=ln(x^2)+6

vs

y=ln(x^3)+6

what change does increasing the power have?

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- Mar 2nd 2010, 03:07 PMp4priGraphs
Hi,

I was wondering how increasing the power of an equation would transform a graph?

e.g

y=ln(x^2)+6

vs

y=ln(x^3)+6

what change does increasing the power have? - Mar 2nd 2010, 08:25 PMKasper
A major change is that the graph will be defined for negative x when x has an even power.

Note than the graph of ln(x) is only defined for positive x as you cannot take the logarithm of a negative number. But if you have $\displaystyle y=ln(x^2)$, the graph will be defined for both positive and negative x as a negative value of x will become positive once you square.

Also, the graph will become steeper, due to you taking the natural logarithm of a larger and larger number as you increase the power of x.