Functions can be different when they are defined on different domains, even when the rules are the same.
In cases when a domain is not specified, we would assume the largest possible domain or maximal domain for which the function is defined.
Let us try finding the maximal domain and the corresponding range for the function f(x) equals to square root of ten x.
Let us find the maximal domain first. Since we know that we can only square root positive numbers and zero, the maximal domain of the function is from 0 to positive infinity. How about the range?
Since the lowest point of the graph is at the origin, referring to the graph, for this value of the domain, the range of the function is positive real numbers.