Types of Functions

1. Linear Functions

ELI5: A linear function is like a straight slide in a playground. You either slide straight down or straight up, depending on which end you start from.

Trading Context: Linear functions are often used to denote a constant rate of change. In trading, this could represent a stock that steadily increases or decreases in price.

Real Trading Example: Technical analysts might use a simple trend line (a linear function) on a price chart to gauge the general direction in which a stock is moving. If a stock's price consistently stays above this line, it's seen as being in an uptrend; below the line indicates a downtrend.

2. Quadratic Functions

ELI5: Imagine throwing a ball upwards. It rises fast at first, slows down at the top of its arc, and then starts falling back down. That's what a quadratic function looks like.

Trading Context: Quadratic functions can represent parabolic moves in the market. These moves start slow, accelerate, and then decelerate.

Real Trading Example: Sometimes stocks experience parabolic moves, often due to hype or extreme bullish sentiment. These are dangerous to trade because after the fast ascent (the upward throw of the ball), there's often a sharp drop (the fall back to the ground).

3. Exponential Functions

ELI5: Think of a snowball rolling down a hill, getting bigger and bigger. It starts small and grows slowly, but then it starts growing really fast.

Trading Context: Exponential functions represent growth that accelerates over time. In trading, this can represent a stock or asset that is experiencing exponential growth.

Real Trading Example: Companies in a rapid growth phase, like many tech companies in their early years, might see their stock prices rise exponentially. Compound interest in an investment also grows exponentially.

4. Trigonometric Functions

ELI5: Imagine a swing going back and forth, up and down, in a rhythmic manner. That's what trigonometric functions, like sine and cosine, represent.

Trading Context: Trigonometric functions can be used to model periodic or cyclical behaviors in the stock market.

Real Trading Example: Some stocks or commodities have seasonal patterns. For instance, heating oil might rise in price leading up to winter due to increased demand. This cyclical behavior can be modeled using trigonometric functions.

5. Logistic Functions

ELI5: Imagine filling a glass with water. At first, you pour fast, but as it nears the top, you slow down to prevent it from overflowing. The logistic function shows this slowing as you approach a limit.

Trading Context: Logistic functions can model growth that starts fast but then slows down as it approaches a certain level or saturation point.

Real Trading Example: Consider a company that's expanding quickly in a new market. At first, its growth is rapid, but as it captures more of the market, growth slows because there are fewer new customers to acquire. The company's growth curve might resemble a logistic function.

In trading, understanding these functions and patterns can give traders an edge, allowing them to anticipate potential price movements and make more informed decisions.