A decreasing function describes a relationship where the output consistently declines as the input increases. This means that for any two input values, if one is greater than the other, the corresponding output is smaller. Mathematically, a function f is decreasing on an interval I if for every x1 < x2​ in I, f (x1) > f (x2). This type of behavior is visually identified on a graph that slopes downward from left to right.The nature of a function can be analyzed by calculating...

A limit describes the value a function approaches as its input moves closer to a particular point. Even when a function is undefined at a specific value, limits allow us to analyze its behavior near that point. This concept is fundamental in calculus and essential for understanding continuity, derivatives, and integrals.Mathematically, a function f(x) has a limit L at x = a if its values L approach x as x gets arbitrarily close to a. This is written as:This notation expresses that the function...

Persuasion is the process of changing our attitude toward something based on some kind of communication. Much of the persuasion we experience comes from outside forces. How do people convince others to change their attitudes, beliefs, and behaviors? What communications do you receive that attempt to persuade you to change your attitudes, beliefs, and behaviors?

One influential perspective on what motivates people's behavior is detailed in Tory Higgin's self-discrepancy theory (Higgins, 1987). He proposed that people hold disagreeing internal representations of themselves that lead to different emotional states.  

Social traps are negative situations where people get caught in a direction or relationship that later proves to be unpleasant, with no easy way to back out of or avoid. The concept was orignally introduced by John Platt who applied psychology to Garrett Hardin's "Tragedy of the Commons", where in New England herd owners could let their cattle graze in the common ground. This situation seems like a good idea, but an individual could have an advantage. If they owned...

When observing how a curve behaves near a specific point along the horizontal axis, there are cases where the curve’s height increases or decreases without limit as the position draws closer to that point. The curve does not settle at any particular value; instead, the values grow more extreme—upward or downward—the nearer they get. No defined value exists exactly at that location, yet the surrounding behavior becomes more dramatic, indicating a sharp change in direction.The...