Algebraic Functions

A function is a rule or mapping that assigns exactly one output (y value) to each input (x value). In short: x → y.

Functions are one of the most important tools in algebra: with their help, we can describe relationships between quantities.

Basic Concepts of Functions

• Domain: the x values for which the function is defined.
• Range: the y values that the function can take.
• Function value: if x = 2, then f(2) is the function's value at 2.
• Mapping: the function assigns a unique image to each element.

Simple Functions

The simplest functions include linear functions, quadratic functions, and constant functions.

This is a linear function, its graph is a straight line.

This is a quadratic function, its graph is parabola-shaped.

This is a constant function that assigns the same y value to every x value.

Representing Functions

Functions are usually represented on a graph, where x values are on the horizontal axis and y values on the vertical axis. The graph helps understand the function's behavior.

Functions in Everyday Life

• If each apple costs 100 forints, the price depends on the quantity: price(x) = 100x.
• If a car travels at constant speed, the distance depends on time: distance(t) = speed × time.
• The change in temperature during the day can also be seen as a function: t → T(t).

Practice Exercise