how do you find a power function that is graphed?

Generally speaking the highest power(degree) tells you how many directions the graph will have

sometimes it can be deceptive because sometimes the graph tries to turn around but does not quite make it.

I am using VERY lay terms here.  

Lets look at some graphs.   a,b,c,...are just constants     LET a>0       

Now I am going to say what I think the degree of each of these will be  (I'll do the top row)

1)  It has five directions so the degree is probably 5 (it has to be odd greater than or equal to 5)

It ends on the right where y is positive so the leading coefficient is positive  

the constant (without an x)  is the y intercept

It is probably     $$y=ax^5+bx^4+cx^3+dx^2+ex-2$$

2)  4 directions ends down so probably      $$y=-ax^4+bx^3+cx^2+dx+0$$

3)  this one has got a kink - that is where it has tried to turn around but has not quite made it.

the degree is most likely 7                       $$y=-ax^7+bx^6+cx^5+dx^4+ex^3+fx^2+gx-2$$

4)  3 directions      $$y=-ax^3+bx^2+cx+3$$

Maybe you can try the others