For this case what you should know is that all functions tend to infinity when x tends to infinity.
However, there are functions that grow faster than others.
In this case, the function that grows fastest is the one with the highest exponent.
We have then:
g (x) = 5x ^ 500
The exponent of 500 makes the function grow to infinity faster than the other functions.
Answer:
C) g (x) = 5x500
