Can someone please explain how I would do this? Arrange the functions x^1/2, x^2, x^3, and 2^x by relative sizes of their y-values
a.On (0,1)

Question

Can someone please explain how I would do this? Arrange the functions x^1/2, x^2, x^3, and 2^x by relative sizes of their y-values 
a.On (0,1)

loser66 · Answer

just plug x =0  into each of the functions, you can calculate the value of them, then arrange them in increasing or decreasing order
for example, for $$y= x^{\frac{1}{2}}$$ plug x =0,  you have $$0^\frac{1}{2}=0 $$

loser66 · Answer

and then to other functions. for x =0 you have 4 values of functions, arrange them.
for x =1 do the same/
hihihi.... I don't know whether my understanding is right or wrong, just give out what I think.

anonymous · Answer

I'll try, thank you!

loser66 · Answer

let hear other 's opinion. @e.mccormick

e.mccormick · Answer

https://www.desmos.com/calculator/vjm827rwpo Depends on the evaluation point, but yes, they want you to set the x, get the y, and compare those ys.

loser66 · Answer

bingo, thank you e.mccormick!!!

anonymous · Answer

So 1=0^1/2, 1=0^2, 1=0^3, 1=2^0?

e.mccormick · Answer

(0,1) is an interval.  because it says on.

e.mccormick · Answer

"On (0,1)" means $0<x<1$

e.mccormick · Answer

If you look at the point (1,1) on the graph I linked, you can see why they said on that interval.

campbell_st · Answer

a really easy way to do this question is to graph all 4 curves |dw:1368306707413:dw| and the link below is to the best free graphing & geometry package available http://www.geogebra.org/cms/en/