Question

For the graphs on the same axes, y=x, y=x^2, y=x^3, y=x^4, y=x^5, what is the growth pattern and what point of intersection do they have in common?

Is it, aside from y=x, which is kinda in the middle, they are expanding? and they intersect at (0,0) ?

Answer 1

this is what i got from google... wouldn't graph y=x for some reason haha but that would just be diagonally through the (0,0).. so yeah hehe :)

Answer 2

hmmm the graph expands.... when the power is high . y = x is a line

Answer 3

okay yeah :) so would you just say that as the power rises, the functions expand, but y=x is just a line ?

Answer 4

x^n = 1 when x=1, for all n.

x^n = 0 when x=0, for all n except 0

Answer 5

^^^so "what points of intersection" (1, 1) and (0, 0)

Answer 6

ohh haha i see that now :P

same as the last one! hahaha i didn't even see the (1,1) !

Answer 7

okay so would these be correct?

as the power gets bigger, the functions expand (with the exception of y=x, which is a line)

and they intersect at point (0,0) and (1,1) ?

Answer 8

@agent0smith is that right? :)

Answer 9

well they're all increasing, even y=x keeps rising

Bigger powers just rise faster

Answer 10

ohh okay awesome!!! thank you!!! :)

Answer 11

y = (x)(x^n-1) where n is the next graph like a geometric sequence

Answer 12

^ that'd simplify to y=x^n