For the function f graphed as follows, approximate each of...

For the function $f$ graphed as follows, approximate each of the limits and values.
$$
\lim _{x \rightarrow-2^{-}} f(x), \lim _{x \rightarrow-2^{+}} f(x), \lim _{x \rightarrow-2} f(x), \text { and } f(-2) .
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Limit of a Function

This concept refers to the value that a function approaches as the input (x) approaches a certain point. It does not necessarily reflect the function’s value at that point; rather, it describes the behavior of the function as it nears the target value.

One-Sided Limits

These are limits where the approach is restricted to one side of a particular point – either from the left (denoted as x ? a?) or from the right (denoted as x ? a?). One-sided limits are vital when analyzing functions that might behave differently on either side of a point.

Continuity

Continuity at a point means that the function is seamlessly connected at that point; the limit as x approaches the point from either side exists, and it equals the actual function value at that point. Understanding continuity is crucial for determining if a function behaves predictably at every point.

Discontinuity

A discontinuity occurs when a function is not continuous at a certain point. This can happen when one or both one-sided limits do not exist, or they exist but differ from the function's value at that point, leading to cases such as jump discontinuities. Discontinuities highlight points at which the function’s behavior 'jumps' or is undefined.

Transcript

Please give Ace some feedback