Final answer:
To determine which function increases at a faster rate on 0 to infinity, compare the rates of growth of the two functions by comparing their derivatives. In this example, the function y = 2/x increases at a faster rate than y = 1/x.
Step-by-step explanation:
To determine which function increases at a faster rate on 0 to infinity, you can compare the rates of growth of the two functions. One way to do this is to compare their derivatives. If the derivative of one function is consistently greater than the derivative of the other function, then the first function increases at a faster rate.
For example, let's compare the functions y = 1/x and y = 2/x. The derivative for y = 1/x is -1/x^2, and the derivative for y = 2/x is -2/x^2. Notice that the derivative of y = 2/x is twice the derivative of y = 1/x. This means that y = 2/x increases at a faster rate than y = 1/x.
Therefore, in this example, the function y = 2/x increases at a faster rate on 0 to infinity.