I need help in how to determine if something is a powerfunction. I know that it

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I need help in how to determine if something is a powerfunction. I know that it must be able to be put in the formf(x)=Kx^p in order to be a power fucntion but my problem isunderstanding how to get it in that form, so please give methe steps and key to these problems so i can understand how todetermine power functions: y=(x-3)^2 y=(-x^3)^3/6 y=(1/2x)^3 y=(6x^-2)(ex^-3) I get so flustered in how to put these in the right form, ithink its the matter knowing what steps to take, so if you couldplease work these out for me, i have a test wednesday and need toknow how to do these, will rate LIFESAVER!thanks I need help in how to determine if something is a powerfunction. I know that it must be able to be put in the formf(x)=Kx^p in order to be a power fucntion but my problem isunderstanding how to get it in that form, so please give methe steps and key to these problems so i can understand how todetermine power functions: y=(x-3)^2 y=(-x^3)^3/6 y=(1/2x)^3 y=(6x^-2)(ex^-3) I get so flustered in how to put these in the right form, ithink its the matter knowing what steps to take, so if you couldplease work these out for me, i have a test wednesday and need toknow how to do these, will rate LIFESAVER!thanks

Explanation / Answer

If all you need is for the function to be in the form f(x) =Kxp then all you need to do is multiply each of thefunctions out in order to get everything in that form. Then it's a lot easier to see whichfunctions are power functions. First, remember that y and f(x) are the same thing. Soyour generic form for a power function could also be written as y =Kxp. Your first function y = (x-3)2 is the same as y =(x-3)(x-3) Using the FOIL method, where FOIL means first, outside,inside, last, multiply the right side of the equation out. Doing so shows: y = x2 -6x + 9    Because this is apolynomial it is the sum of power functions, but is not a powerfunction. The second function, y = (-x3)3/6 Remember that when you raise something to a power and thething you're raising is already raised to a power then you need tomultiply the powers together. y = -x3*(3/6)= -x9/6=-x3/2 This function IS a power function because it meets the formyou've been given. K here equals -1 and P equals 3/2 For the third function remember that taking a square root of xis the same as raising x to the 1/2 power. rewrite the thirdfunction in this way and use the same rule from the second function tosee that y = [ (1/2)x1/2 ] 3   =(1/2)x3/2 = This too is a power function For the last one, it's probably easier to see when you writeit like: 6x-2ex-3      Rememberthat e is just a real number, so you can add the two powerstogether here and rewrite this like: y = 6ex-5 So the first function is not a power function but the lastthree are. So the first function is not a power function but the lastthree are.

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