How do I know if the limit of a function exists or not from that function's graph. Thanks.

It the graph of a function becomes straighter at + and -infinity, it means that the function behaves linearly in the limit. However there may be other types of limiting behavior that would be harder to detect graphically.

The limit from the right must equal to the limit from the left, the function must be continuous, and f(x) must exist.

SOmething along those lines.


To determine if the limit of a function exists from the graph, there are a few key things to consider.

1. Approach from the left and right: First, examine the behavior of the graph as it approaches the point in question from both the left and right sides. If the function approaches the same value or tends towards the same behavior from both sides, it suggests that a limit may exist at that point.

2. Continuity: Look for any gaps, jumps, or vertical asymptotes in the graph. If the graph has any discontinuities at the point in question, then the limit will not exist.

3. Determining linearity: Consider the overall shape and trend of the graph as you move away from the point. If the graph becomes increasingly straighter or approaches a straight line as you move towards positive or negative infinity, it indicates a linear behavior in the limit. However, note that just because the graph appears linear in certain directions does not guarantee a limit exists.

It is important to note that the graph alone may not always provide a definitive answer about the existence of a limit. Mathematical techniques, such as using the definition or symbolic manipulations, are often required to prove the existence of a limit more rigorously.