Functions and their graphs

Mathematical Thinking I

Functions and their graphs

Dra. Diana Denys Jiménez Suro Dr. Antonio Jesús Sánchez HernándezCampus Estado de México Campus Santa Fe

Domain and Range

The value of one variable quantity, say 𝑦, depends on the value of another variable quantity, which we might call 𝑥. We say that “𝑦 is a function of 𝑥” and write this symbolically as

Definition

A function 𝑓 from a set 𝐷 to a set 𝑌 is a rule that assigns a unique (single) element 𝑓(𝑥)𝜖𝑌 to each element 𝑥𝜖𝐷.

Circle

Linear functions

A function of the form 𝑓(𝑥)=𝑚𝑥+𝑏, for constants 𝑚 and 𝑏, is called a linear function. The figure shows an array of lines 𝑓(𝑥)=𝑚𝑥 where 𝑏=0, so these lines pass through the origin. The function 𝑓(𝑥)=𝑥 where 𝑚=1 and 𝑏=0 is called the identity function.

Power functions

A function 𝑓(𝑥)=𝑥𝑎, where 𝑎 is a constant, is called a power function. There are several important cases to consider

Polynomials

A function 𝑝 is a polynomial if 𝑝(𝑥)=𝑎𝑛𝑥𝑛+𝑎𝑛−1𝑥𝑛−1+⋯+𝑎1𝑥+𝑎0

Referencias

Thomas

Cálculo de una variable13a. Edición, PEARSON

2015

Prado, et al

Modelación matemática fundamental1a. Edición, PEARSON

2019

Stewart

Cálculo trascendentes tempranas8a. Edición, CENGAGE

2018

Elaboración

Antonio Jesús Sánchez Hernández Campus Santa Fe ajsanchez@tec.mx

Diana Denys Jiménez Suro Campus Estado de México ddjimenez@tec.mx