Consider these four functions. Choose the one which will be the greatest as x → ∞. A) h (x) = 3x B) f (x) = x25 C) g (x) = 5x500 D) k (x) = x8 + 8000

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