linear functions
[ˈlɪniər ˈfʌŋkʃənz]
nounpl: linear functions
funções lineares
1. Mathematical functions of the form f(x) = mx + b, where the graph is a straight line with constant slope m and y-intercept b
Linear functions are among the simplest and most important functions in algebra and calculus.
Funções lineares são entre as mais simples e importantes funções em álgebra e cálculo.
2. In higher mathematics, functions that satisfy the properties of additivity and homogeneity, commonly used in linear algebra
In vector spaces, linear functions map vectors to scalars while preserving linear combinations.
Em espaços vetoriais, funções lineares mapeiam vetores para escalares preservando combinações lineares.
3. Functions whose output is directly proportional to their input with no exponential or polynomial terms
The relationship between distance and time at constant speed represents a linear function.
A relação entre distância e tempo em velocidade constante representa uma função linear.
Linear functions are fundamental in educational mathematics curricula in both Brazil and the United States. In Brazilian schools, they are typically introduced in middle school (ensino fundamental II) as part of algebra instruction. The term is standardized across Portuguese-speaking countries due to international mathematical conventions. In the USA, linear functions are a cornerstone of high school algebra courses and are essential for STEM education.
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