]In “Graph Square root and Cube root Function” , How can I tell a graph has Domain and Range are all real numbers or x ≥ 0 and y ≥ 0 ?? Only by graph?
The graph should meet your expectations based on the function itself. A square root function will always have some exclusion and so the domain will never be all real numbers. Any value of x that makes the contents of the square root negative will be excluded from the domain. So, solve (stuff inside square root) < 0, and those are your excluded values.
The cube root function has no restrictions. So, its domain (as long as the contents of the root is a simple polynomial) is always “all real numbers”.
As far as range, for the square root function, when you graph within the restrictions of the domain, you will see the range. The starting point is the place where the root is zero (about to be negative). And the rest of the range is either +infinity or -infinity.
For the range of the cube root function, it is all real numbers, as you can see the curve extending in both directions