Algebra-2

Question Analysis
This question involves describing the end behavior of the logarithmic function as becomes very large.
The main focus is on understanding how the function’s value changes as the input grows without bound.

Key Concept Explanation
End behavior describes how a function’s value behaves as approaches extreme values (like or ). For (where , like ):
As gets larger and larger (approaches positive infinity, ), the value of also increases—but it increases slowly. However, it never stops increasing; it continues to grow without bound.
This means the function’s value approaches positive infinity as . (Note: If , the behavior is different, but all common logarithmic bases in Algebra 2 are .)

Step-by-Step Solution
1. Identify the base of : , which is a common "growth" base for logarithms.
2. Analyze function values as increases:
When : .
When : .
When :