For the graph attached inside (y=x^1/2, y=x^1/3, y=x^1/4, y=x^1/5), what is the growth pattern? And which point do they have in common (intersection)?

Is it, they decrease from x^1/2 to x^1/5?

and they have the common point of (0,0) ?

Question

For the graph attached inside (y=x^1/2, y=x^1/3, y=x^1/4, y=x^1/5), what is the growth pattern? And which point do they have in common (intersection)?

Is it, they decrease from x^1/2 to x^1/5?

and they have the common point of (0,0) ?

anonymous · Answer

graph! :)

jim_thompson5910 · Answer

you have mistakenly graphed (x^1)/2, (x^1)/3, (x^1)/4, (x^1)/5

jim_thompson5910 · Answer

since you should have typed in

x^(1/2), x^(1/3), x^(1/4), x^(1/5)

anonymous · Answer

aww darn :(

lemme fix that haha

anonymous · Answer

okay so it should look like this?

jim_thompson5910 · Answer

the computer is following PEMDAS

because exponentiation is before division, this means that x^1 is evaluated first, then you divide

So that's why x^1/2 = (x^1)/2

jim_thompson5910 · Answer

much better graph

anonymous · Answer

okay yay :)

and i'll definitely keep that in mind for the future!!! :)

anonymous · Answer

so would it that from x^(1/2)-x^(1/5), they decrease?

jim_thompson5910 · Answer

yes, x^(1/2) has a larger growth rate compared to x^(1/3)

x^(1/3) has a larger growth rate compared to x^(1/4)

etc etc

anonymous · Answer

okay :) 

and do they intersect at the point (1.5, 1) ?

agent0smith · Answer

Common point at x=1 too... the n-th root of 1 is 1.

anonymous · Answer

oh so would it just be x=1? or would you say (1,0) ?

jim_thompson5910 · Answer

double click where it looks like they are all crossing

jim_thompson5910 · Answer

that will make the graph zoom in

agent0smith · Answer

(0,0) and (1,0)

jim_thompson5910 · Answer

not (1,0)

agent0smith · Answer

"the n-th root of 1 is 1." so x^(1/n) will always equal 1 when x=1

jim_thompson5910 · Answer

and move the mouse near the point of intersection, the coordinates of the point will be listed in the upper right corner

anonymous · Answer

ohh they intersect at (1,1) ?

jim_thompson5910 · Answer

yes

jim_thompson5910 · Answer

and also (0,0)

anonymous · Answer

whoah i never knew you could zoom like that!

anonymous · Answer

okay great!! :) 

so that answers it all for this problem right? :O

jim_thompson5910 · Answer

the zoom tool is on the left side as well

jim_thompson5910 · Answer

and yes I think so

anonymous · Answer

okay yayy!! :) thank youu!! :)

and yeah i was trying to use that earlier, but it zooms from (0,0) so i couldn't get to the point (1,1) lol :P

agent0smith · Answer

You can zoom individually along the x axis or y axis, it's awesome.

anonymous · Answer

okay awesome!! :) I'll definitely keep that in mind!! i was trying to zoom earlier and it wasn't working lol now i know how to do it! yay :)

agent0smith · Answer

mouse wheel zooms btw, if your mouse has one

anonymous · Answer

oh okay yeah i have one :)

woo! always learning new things hehe