Define a cube root function in METAPOST

Question

I want to draw the graph of the cube root function $f(x) = \sqrt[3]{x+1}$ by using METAPOST. However, when I use the vardef macro as follows

vardef f(expr x) = (x+1)**(1/3) enddef;

It seems to be invalid. How can we define this function in METAPOST?

Answer 1

According to your comment, the part you needed help for was to have the cube root work even for negative numbers. What about this?

vardef cuberoot(expr x) = if x < 0: -1* fi ((abs(x))**(1/3)) enddef;
vardef f(expr x) = cuberoot(x+1) enddef;

show f(-1);
show f(2);
show f(1);
show f(-3);

end

Output:

>> 0
>> 1.44225
>> 1.25992
>> -1.25992

Note: instead of if x < 0: -1* fi, you can also use if x < 0: - fi (it is possibly a tiny bit faster).