Question

Let g be a function that is decreasing for x > 0. What can be said about the behavior of g as x approaches positive infinity?

1) g approaches a finite limit as x approaches positive infinity
2) g approaches negative infinity as x approaches positive infinity
3) g approaches positive infinity as x approaches positive infinity
4) g approaches zero as x approaches positive infinity

Answer 1

A function g that is decreasing for x > 0 will approach negative infinity as x approaches positive infinity.

Step-by-step explanation:

A function g that is decreasing for x > 0 will approach negative infinity as x approaches positive infinity.

This can be understood by considering the behavior of the function as x gets larger and larger. Since g is decreasing, the function values will get smaller and smaller. As x approaches positive infinity, the function values will approach negative infinity.

Therefore, option 2) g approaches negative infinity as x approaches positive infinity is the correct answer.