Question

Graph y=x^-1, y=x^-2, y=x^-3, y=x^-4 on the same coordinate axes.

What are three observations about the graph?
(general shapes, decreasing/increasing, concave up/down, asymptotes..)

I have the graph attached (courtesy of google :P )

how can i determine the observations? :) and did i even enter it into google correctly? :P

Answer 1

graph!

Answer 2

Looks right https://www.google.com/search?q=1%2Fx%2C+1%2Fx%5E2%2C+1%2Fx%5E3%2C+1%2Fx%5E4&oq=1%2Fx%2C+1%2Fx%5E2%2C+1%2Fx%5E3%2C+1%2Fx%5E4&aqs=chrome..69i57j69i58j0l4.30132j0j4&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8

Asymptotes should be easy to spot, same for all of 'em

Answer 3

would the asymptote be x=0 ?

Answer 4

That's the vertical, what about the horizontal

Answer 5

would it also be y=0?

Answer 6

All are concave up where x>0,

the even powers are concave up where x<0,

odd powers are concave down where x<0

Answer 7

okay awesome! :)

and would the general shape be referring to whether it's a sin, cos, tan graph, etc ?

Answer 8

No, just... idk, hyperbola i guess.

Answer 9

ohh okay haha

parabola would be if it's a U-shape right?

Answer 10

Yep

Answer 11

going up or down?

Answer 12

lol i clicked delete by accident :P

Answer 13

okay awesome!! thank you so much!!! :)

Answer 14

Welcome :)