4.7k views
1 vote
As x gets closer and closer to (but stays less than) 1, g(x) gets as close as we want to:

a) g(1)
b) g([infinity])
c) g(−[infinity])
d) g(0)

User Ranguard
by
8.7k points

1 Answer

5 votes

Final answer:

The function g(x) as x approaches 1 from the left is likely to approach g(1), given that g(x) is defined and continuous at that point, similar to the behavior of horizontal asymptotes.

Step-by-step explanation:

The behavior of a function as x approaches a particular value is known as a limit. In the question provided, we are asked to determine the behavior of the function g(x) as x approaches 1 from the left (staying less than 1). Without the specific function g(x) provided, we must rely on general knowledge about limits and the concept of horizontal asymptotes. If the function g(x) has a horizontal asymptote or smooth behavior as x approaches 1, then g(x) would get closer and closer to g(1). This is the case for a function like y = 1/x, where as x approaches a value (x ≠ 0), y approaches a finite limit. This suggests that for g(x), as x gets closer to 1, the function value would converge to g(1), assuming it's defined and continuous at that point.

User VanBantam
by
8.1k points