4. ¿Cómo determino el dominio de una función?
El dominio de una función (Dom f), será el conjunto de todos los
elementos para los cuales está definida la función, es decir, los
valores que toma la variable independiente.
5. Recorrido de una
función
El recorrido de una función (Rec f)
será el conjunto de valores que
toma la variable dependiente (𝑦),
es decir, todos los valores que
son imagen de algún valor de la
variable independiente.
¿Cómo determino el
recorrido de una función?
Una forma de obtener el recorrido de
una función es ”despejar”, en la
expresión algebraica de la función la
variable independiente x ”en función”
de la variable dependiente y.
Luego, se debe analizar para qué
valores reales estará definida la
expresión.
8. Ejercicio. Sea la función 𝑓 𝑥 = 𝑥 − 6, ¿Cuál es el dominio y recorrido
de la función?
9. Función constante (color naranja)
𝑓 𝑥 = 𝑐, 𝑐 ∈ ℝ
Función que tiene una única intersección
en el eje y
Función lineal (color verde)
𝑓 𝑥 = 𝑚𝑥,
𝑚 ∈ ℝ − {0}
Función que siempre pasa por el
origen
Función afín (color rojo y azul)
𝑓 𝑥 = 𝑚𝑥 + 𝑛, 𝑚, 𝑛 ∈ ℝ, 𝑛 ≠ 0
Función que corta al eje y en el punto
(0, 𝑛)
Corresponde a ser una traslación de
la función lineal
11. i) Plan Tarifa plana: tiene un costo de $120 el minuto en todo horario.
ii) Plan optimiza: tiene un cargo fijo de $4000 más $60 el minuto.
Resolver:
a) Escribir la tarifa que modela cada plan.
b) Clasificar que tipo de funciones son: lineal o afín.
c) Si una persona habla 100 minutos al mes ¿Cuánto paga en cada
plan? ¿Qué plan le conviene contratar?
Problema. Una compañía telefónica ofrece dos planes:
12. Problema. La tarifa de cierta
compañía de telefónica consta de un
cargo fijo mensual de $9.000 más un
cargo de $50 por minuto que se
habla. Si durante los primeros 240
minutos esta tarifa se modela
mediante una función de la forma
𝑓 (𝑥) = 𝑚𝑥 + 𝑛 ,
¿Cuál de las siguientes gráficas
representa mejor a la gráfica de f ?
18. Dominio y
recorrido
(Casos
generales)
La función lineal
siempre tendrá como
dominio y recorrido
los número reales
El dominio y recorrido
de una función
racional, serán todos
los reales, excepto
los valores que
anulan el
denominador.
19. Pendiente. Sea la función 𝑓 𝑥 =
2𝑥
𝑥−4
, ¿Cuál es el recorrido de la
función?
20. ACTIVIDAD
1.- Sea la función 𝑓 𝑥 =
𝑥+1
𝑥+2
, ¿Cuál es el dominio y recorrido de
la función?
2.- Sea la función 𝑓 𝑥 =
𝑥
2
, ¿Cuál es el dominio y recorrido de
la función?
21. 1.- Sea la función 𝑓 𝑥 =
𝑥+1
𝑥+2
, ¿Cuál es el dominio de la función?
22. 1.- Sea la función 𝑓 𝑥 =
𝑥+1
𝑥+2
, ¿Cuál es el recorrido de la función?
23. 2.- Sea la función 𝑓 𝑥 =
𝑥
2
, ¿Cuál es el dominio y recorrido de la
función?
31. “The closest planet to the Sun
and the smallest one in the
Solar System”
Literature Review
—Lisa Jane —Angelina Jones
“Venus has a beautiful name
and is the second planet from
the Sun. It’s terribly hot”
32. Task Jan Feb Mar Apr May
01
02
03
04
05
06
Schedule
33. Mercury is the closest
planet to the Sun
Venus has a beautiful
name, but it’s hot
Despite being red, Mars is
a cold place
Saturn is the ringed one
and a gas giant
Teaching Functions and Tasks
Technological Motivational
Academic Pedagogical
35. Rol Functions Students Training
Adviser 1 Academic 20-25 Disciplinary
Adviser 2 Pedagogical 20-25 Education Distance
Adviser 3 Technological 20-25 ICT
Multifunctional Model
36. Rol Functions Number of students Type of training
Adviser Academic and pedagogical 20-25
Discipline, Distance
Education and ICT
Tutor
Technological, motivational,
organizational and
administrative
40-55
Distance Education
and ICT
Bifunctional Model
37. Task Analysis
Programming 15,0% Students
15,0%
Age
5,0%
Language
15,0%
Platform
5,0%
Assigned 45,0%
To modify this graph, click on it, follow the link, change the data and paste the new graph here
38. Mercury is the closest
planet to the Sun
Despite being red, Mars is
a cold place
It’s the biggest planet in
the Solar System
Neptune is the farthest
planet from the Sun
Venus has a beautiful
name, but it’s hot
Saturn is the ringed one
and a gas giant
Validation of Tutoring Models
Administrative tasks Organizational tasks
Advisor information Tasks by role
Motivational tasks
Data of the courses
39. Value Value
Mercury & Mars Earth
● The third from the Sun
● It harbors life
● It’s where we live on
● 110
● 100
● 333
● 029
● 200
● 080
Saturn
● It has several rings
● It’s a gas giant
● 018
● 382
● 003
● 033
You Can Use a Table
40. Mars is the fourth planet from the
Sun and the second-smallest
planet in the Solar System, being
only larger than Mercury.
To modify this graph, click on it, follow the link, change the data and paste the new graph here
Online Teaching
Mars
Society Health Language Technology Computing
0
10
20
30
40
50
41. Planet Venus has a
beautiful name
Canada
Greater Use of Distance Education
It’s a gas giant and
the biggest planet
Russia
Despite being red,
Mars is a cold place
Chile
It’s composed of
hydrogen and helium
Australia
It’s the closest planet
to the Sun
South Africa
20%
15%
10%
35%
20%
42. A Timeline Always Works Well
Distance learning was
first invented
1895
Internet becomes a
household name
1989
Computer assisted
learning center
1982
3,5 million students
using E-learning
2006
43. Students enrolled in courses at degree-granting
postsecondary institutions in 2017
19.7 M
44. Students took at least one but
not all of their courses online
Students enrolled in exclusively
distance education
Students took more than half
of their courses online
3,2M (19,5%)
2,2M (13,3%) 274,211 (9,1%)
45. Helena Patterson
Anton Smith
John Doe
You can replace the star
on the screen with a
picture of this person You can replace the star
on the screen with a
picture of this person
You can replace the star
on the screen with a
picture of this person
Our Team
46. Conclusions
The closest planet to the Sun and the
smallest one in the Solar System—it’s
only a bit larger than the Moon
1
It’s terribly hot—even hotter than
Mercury—and its atmosphere is
extremely poisonous
2
47. ● AUTHOR (YEAR). Title of the publication. Publisher
● AUTHOR (YEAR). Title of the publication. Publisher
● AUTHOR (YEAR). Title of the publication. Publisher
● AUTHOR (YEAR). Title of the publication. Publisher
● AUTHOR (YEAR). Title of the publication. Publisher
Bibliographical References
48. You can replace the image on the
screen with your own work. Just
delete this one, add yours and
center it properly
Desktop Software
49. You can replace the image on the
screen with your own work. Just
delete this one, add yours and
center it properly
Mobile Web
50. You can replace the image on the
screen with your own work. Just
delete this one, add yours and
center it properly
Tablet App
51. CREDITS: This presentation template was created by
Slidesgo, including icons by Flaticon, and infographics &
images by Freepik.
Please keep this slide for attribution.
Thanks!
Do you have any questions?
addyouremail@freepik.com
+91 620 421 838 yourcompany.com
55. Alternative Resources
Photo
● Teacher and kids hugging outdoors close-up
● Kids hugging their teacher
● Teacher smelling a bouquet of flowers with copy space
● Teacher standing next to a blackboard with copy space
● Happy teacher helping her students
56. Resources
● Business infographic with different
sheets of paper
● Instagram stories template pattern
● Abstract brush stroke pastel pattern
● Abstract brush stroke pattern
● Schedule with nice notes
Vectors
Photos
● Beautiful young female with paper cup
in office
● Teacher writing on white board
● Portrait female teacher in class
● Daughter and mom hugging on couch
● Black father feeding son with croissant
● Smiley teacher standing in classroom
● Teacher hugging a student with copy
space
