I would like to know manually how to draw the family functions.
I try to find the pictures of the graph, apparently i can find only $x^3$ graph photo below.
what I want to know is how to work out and get this graph?
i have questions like
function is $f(x)=x^n$
1. $x^1$
2. $x^{-1}$
3. $x^{-1/4}$
4. $x^{1/4}$
5. $x^{-2/3}$
but I would like to know how to draw the graph by manually solve the functions.
Hope my question is clear.
Thanks in advance.
eg. $x^3$
You can plot functions using Wolfram|Alpha, e.g. $x^{-2/3}$. If you want to do it by hand, make a table of some function values in the range of interest, mark the corresponding points in a coordinate system and try to connect them with a smooth curve, using whatever you may now about the function, e.g. zeros, poles, extrema etc.