Mathematical Functions Overview
This page provides a comprehensive overview of various types of mathematical functions, crucial for first-year high school students. The functions covered include linear, quadratic, polynomial, rational, and exponential functions.
Definition: A function in mathematics is a relation between a set of inputs (domain) and a set of possible outputs (range), where each input corresponds to exactly one output.
Linear Functions
Linear functions are the most basic type of function, represented by the equation y = ax + b.
Example: y = 3x - 2 is a linear function where a = 3 and b = -2.
Quadratic Functions
Quadratic functions are characterized by a second-degree term (x²) and are represented by the general form y = ax² + bx + c.
Highlight: The graph of a quadratic function is always a parabola.
Several forms of quadratic functions are presented:
- Standard form: y = ax² + bx + c
- Factored form: y = a(x - x₁)(x - x₂)
- Vertex form: y = a(x - x₀)² + y₀
Vocabulary: The vertex of a parabola is the point where it reaches its maximum or minimum value.
Polynomial Functions
Polynomial functions are extensions of quadratic functions, including higher-degree terms.
Example: y = -2x³ + 1 is a cubic polynomial function.
Rational Functions
Rational functions are fractions of polynomials.
Example: y = (3x² + 2) / (3x² + 8x + 4) is a rational function.
Exponential Functions
Exponential functions have a variable in the exponent.
Example: y = 3ˣ is an exponential function.
Highlight: Understanding these different types of funkcje matematyczne is crucial for success in Funkcje Klasa 1 liceum Sprawdzian (Functions Class 1 High School Test).
