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Matemáticas I

La recta

Ecuación de la recta

Rectas paralelas al eje ox y al oy

Ejercicios de Funciones Resueltos para ESO y Bachillerato - PDF Gratis

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Ejercicios de Funciones Resueltos para ESO y Bachillerato - PDF Gratis

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A comprehensive guide to mathematical functions and their properties, focusing on ejercicios de funciones resueltos and various function types. This material covers essential concepts from basic to advanced function analysis, including exponential, logarithmic, and piecewise functions.

• Detailed coverage of function domains, symmetry, and asymptotes
• In-depth analysis of funciones exponenciales y logarítmicas ejercicios resueltos PDF
• Comprehensive examples of funciones definidas a trozos ejercicios resueltos
• Step-by-step solutions for graphing and analyzing functions
• Essential concepts for students studying ejercicios de funciones 3o ESO through advanced levels

9/5/2023

10956

T
1. Dom (-00, 3) U (3,00)
2. simetría
3. A. sínt : AV- x= 3
AH-y=S
AO- #
4. cortes: con Oy-
(0,2'5)
con ox (-2,0), (2,0)
5. Monot crec - (-

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Page 8: Trigonometric Functions

This page focuses on trigonometric functions, particularly sine and cosine:

Graphs of y = sin x and y = cos x are shown, highlighting their periodic nature.
The effect of changing the frequency is demonstrated with y = sin 2x.

Vocabulary: Period - the length of one complete cycle of a trigonometric function.

Highlight: Trigonometric functions are fundamental in modeling periodic phenomena in physics, engineering, and other sciences.

Example: The graph of y = sin 2x has twice the frequency of y = sin x, completing a full cycle in π radians instead of 2π.

This information is crucial for solving advanced ejercicios de funciones 2 ESO pdf con soluciones involving trigonometric functions.

Ver

Page 2: Irrational and Exponential Functions

This page covers two important types of functions:

Irrational Functions:

These are functions that involve square roots or other roots.
The domain of irrational functions is typically restricted to non-negative values under the root.

Example: For f(x) = √x, the domain is [0, ∞).

Exponential Functions:

These functions have the variable in the exponent.
Common forms include y = 2^x and y = e^x.
The domain of exponential functions is all real numbers (-∞, +∞).

Highlight: Exponential functions grow rapidly, which is important in many real-world applications.

Example: For y = 2^x, some key points are (0, 1), (1, 2), (-1, 0.5).

This page provides essential information for solving funciones exponenciales ejercicios resueltos pdf 4 eso.

Ver

Page 12: Domain Calculation Exercises

This page provides a series of exercises for calculating the domains of various functions:

Irrational functions: Ensure the radicand is non-negative.
Rational functions: Exclude values that make the denominator zero.
Logarithmic functions: Ensure the argument is positive.
Composite functions: Consider restrictions from all components.

Example: For f(x) = √(x - 6), the domain is [6, ∞) because x - 6 ≥ 0.

Highlight: These exercises cover a wide range of function types and complexity levels, providing excellent practice for domain calculation.

This page is essential for mastering recorrido de una función a trozos and other function analysis skills.

Ver

Page 10: Domain Calculation

This page focuses on calculating the domain of various function types:

Polynomial functions: Domain is all real numbers.
Rational functions: Domain excludes values that make the denominator zero.
Irrational functions: Domain includes values that make the radicand non-negative.
Logarithmic functions: Domain includes values that make the argument positive.

Example: For f(x) = √(7-4x), the domain is (-∞, 7/4] because 7-4x ≥ 0.

Highlight: Determining the domain is a crucial first step in analyzing any function.

This page provides essential techniques for solving dominio de funciones a trozos ejercicios resueltos.

Ver

Page 3: Function Types and Their Graphs

This page presents a visual overview of various function types and their characteristic graphs:

Linear function: y = x
Quadratic function: y = x²
Reciprocal function: y = 1/x
Square root function: y = √x
Exponential function: y = e^x
Logarithmic function: y = ln x
Trigonometric function: y = sin x

Highlight: Understanding the shape and behavior of these basic functions is crucial for analyzing more complex functions and solving ejercicios de funciones 1 ESO pdf con soluciones.

Definition: The domain of a function is the set of all possible input values (x-values) for which the function is defined and will produce a real output value.

Ver

Page 5: Symmetry and Asymptotes

This page delves deeper into two key concepts of function analysis:

Symmetry:

Symmetry with respect to the y-axis
Symmetry with respect to the origin

Asymptotes:

Vertical asymptotes: x = a
Horizontal asymptotes: y = a (up to two possible)
Oblique asymptotes: y = mx + n (up to two possible)

Definition: An asymptote is a line that a curve approaches but never touches as it goes to infinity.

Highlight: Understanding asymptotes is crucial for sketching accurate graphs of rational and transcendental functions.

This page provides essential knowledge for solving estudio de funciones ejercicios resueltos pdf problems.

Ver

Page 6: Logarithmic Functions

This page focuses on logarithmic functions, which are the inverse of exponential functions:

The general form is y = log_a(x), where a is the base.
Two common forms are discussed: y = log x (base 10) and y = ln x (natural logarithm, base e).
The domain of logarithmic functions is (0, ∞).

Example: For y = ln x, some key points are (1, 0), (e, 1), (e², 2).

Highlight: Logarithmic functions grow slowly compared to exponential functions, which makes them useful in many scientific and financial applications.

This information is crucial for solving funciones logarítmicas ejercicios resueltos pdf problems.

Ver

Page 9: Absolute Value Functions

This page explains how to work with absolute value functions:

Set the expression inside the absolute value signs to zero.
Solve the resulting equation.
Use a number line to study the sign in each region.
Express the function as a piecewise function.

Example: For y = |x - 2|:

x - 2 = 0

x = 2

Analyze signs: negative for x < 2, positive for x > 2

y = { -(x - 2), x < 2 x - 2, x ≥ 2 }

Highlight: Absolute value functions are important in modeling situations where the magnitude of a quantity is more important than its sign.

This page provides valuable insights for solving funciones definidas a trozos ejercicios resueltos 1 Bachillerato problems.

Ver

Page 1: Function Analysis Techniques

This page introduces key concepts for analyzing functions graphically:

Domain: The range of x-values for which the function is defined.
Symmetry: Identifying if a function has symmetry around the y-axis, x-axis, or origin.
Asymptotes: Vertical, horizontal, and oblique asymptotes are discussed.
Intersections: Points where the function crosses the x and y axes.
Monotonicity: Intervals where the function is increasing or decreasing.
Extrema: Maximum and minimum points of the function.
Concavity: Regions where the function is concave up or down.
Inflection points: Where the concavity of the function changes.

Example: For a given function, the domain is (-∞, 3) ∪ (3, ∞), with a vertical asymptote at x = 3 and a horizontal asymptote at y = 5.

Highlight: Understanding these properties is crucial for sketching accurate graphs of functions and solving ejercicios de funciones 3o ESO.

Ver

Page 4: Function Transformations and Piecewise Functions

This page covers two important topics:

Function Transformations:

Changing x to -x reflects the function over the y-axis.
Examples are provided for various function types (quadratic, square root, exponential, trigonometric).

Example: For f(x) = x², f(-x) = (-x)² = x², showing that this function is symmetric about the y-axis.

Piecewise Functions:

These are functions defined differently for different intervals of the domain.
The page shows how to analyze and graph piecewise functions.

Highlight: Piecewise functions are important in modeling real-world scenarios where behavior changes at certain points.

This information is valuable for tackling funciones definidas a trozos ejercicios resueltos pdf problems.

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Asignaturas

Matemáticas I

La recta

Ecuación de la recta

Rectas paralelas al eje ox y al oy

Ejercicios de Funciones Resueltos para ESO y Bachillerato - PDF Gratis

Nathalie

@nathalieper_

380 Seguidores

Seguir

I'll help create SEO-optimized summaries for this mathematical content. Let me break this down page by page.

9/5/2023

10956

1° Bach

Matemáticas I

726

Page 8: Trigonometric Functions

This page focuses on trigonometric functions, particularly sine and cosine:

Graphs of y = sin x and y = cos x are shown, highlighting their periodic nature.
The effect of changing the frequency is demonstrated with y = sin 2x.

Vocabulary: Period - the length of one complete cycle of a trigonometric function.

Highlight: Trigonometric functions are fundamental in modeling periodic phenomena in physics, engineering, and other sciences.

Example: The graph of y = sin 2x has twice the frequency of y = sin x, completing a full cycle in π radians instead of 2π.

This information is crucial for solving advanced ejercicios de funciones 2 ESO pdf con soluciones involving trigonometric functions.

Page 2: Irrational and Exponential Functions

This page covers two important types of functions:

Irrational Functions:

These are functions that involve square roots or other roots.
The domain of irrational functions is typically restricted to non-negative values under the root.

Example: For f(x) = √x, the domain is [0, ∞).

Exponential Functions:

These functions have the variable in the exponent.
Common forms include y = 2^x and y = e^x.
The domain of exponential functions is all real numbers (-∞, +∞).

Highlight: Exponential functions grow rapidly, which is important in many real-world applications.

Example: For y = 2^x, some key points are (0, 1), (1, 2), (-1, 0.5).

This page provides essential information for solving funciones exponenciales ejercicios resueltos pdf 4 eso.

Page 12: Domain Calculation Exercises

This page provides a series of exercises for calculating the domains of various functions:

Irrational functions: Ensure the radicand is non-negative.
Rational functions: Exclude values that make the denominator zero.
Logarithmic functions: Ensure the argument is positive.
Composite functions: Consider restrictions from all components.

Example: For f(x) = √(x - 6), the domain is [6, ∞) because x - 6 ≥ 0.

Highlight: These exercises cover a wide range of function types and complexity levels, providing excellent practice for domain calculation.

This page is essential for mastering recorrido de una función a trozos and other function analysis skills.

Page 10: Domain Calculation

This page focuses on calculating the domain of various function types:

Polynomial functions: Domain is all real numbers.
Rational functions: Domain excludes values that make the denominator zero.
Irrational functions: Domain includes values that make the radicand non-negative.
Logarithmic functions: Domain includes values that make the argument positive.

Example: For f(x) = √(7-4x), the domain is (-∞, 7/4] because 7-4x ≥ 0.

Highlight: Determining the domain is a crucial first step in analyzing any function.

This page provides essential techniques for solving dominio de funciones a trozos ejercicios resueltos.

Page 3: Function Types and Their Graphs

This page presents a visual overview of various function types and their characteristic graphs:

Linear function: y = x
Quadratic function: y = x²
Reciprocal function: y = 1/x
Square root function: y = √x
Exponential function: y = e^x
Logarithmic function: y = ln x
Trigonometric function: y = sin x

Highlight: Understanding the shape and behavior of these basic functions is crucial for analyzing more complex functions and solving ejercicios de funciones 1 ESO pdf con soluciones.

Definition: The domain of a function is the set of all possible input values (x-values) for which the function is defined and will produce a real output value.

Page 5: Symmetry and Asymptotes

This page delves deeper into two key concepts of function analysis:

Symmetry:

Symmetry with respect to the y-axis
Symmetry with respect to the origin

Asymptotes:

Vertical asymptotes: x = a
Horizontal asymptotes: y = a (up to two possible)
Oblique asymptotes: y = mx + n (up to two possible)

Definition: An asymptote is a line that a curve approaches but never touches as it goes to infinity.

Highlight: Understanding asymptotes is crucial for sketching accurate graphs of rational and transcendental functions.

This page provides essential knowledge for solving estudio de funciones ejercicios resueltos pdf problems.

Page 6: Logarithmic Functions

This page focuses on logarithmic functions, which are the inverse of exponential functions:

The general form is y = log_a(x), where a is the base.
Two common forms are discussed: y = log x (base 10) and y = ln x (natural logarithm, base e).
The domain of logarithmic functions is (0, ∞).

Example: For y = ln x, some key points are (1, 0), (e, 1), (e², 2).

Highlight: Logarithmic functions grow slowly compared to exponential functions, which makes them useful in many scientific and financial applications.

This information is crucial for solving funciones logarítmicas ejercicios resueltos pdf problems.

Page 9: Absolute Value Functions

This page explains how to work with absolute value functions:

Set the expression inside the absolute value signs to zero.
Solve the resulting equation.
Use a number line to study the sign in each region.
Express the function as a piecewise function.

Example: For y = |x - 2|:

x - 2 = 0

x = 2

Analyze signs: negative for x < 2, positive for x > 2

y = { -(x - 2), x < 2 x - 2, x ≥ 2 }

Highlight: Absolute value functions are important in modeling situations where the magnitude of a quantity is more important than its sign.

This page provides valuable insights for solving funciones definidas a trozos ejercicios resueltos 1 Bachillerato problems.

Page 1: Function Analysis Techniques

This page introduces key concepts for analyzing functions graphically:

Domain: The range of x-values for which the function is defined.
Symmetry: Identifying if a function has symmetry around the y-axis, x-axis, or origin.
Asymptotes: Vertical, horizontal, and oblique asymptotes are discussed.
Intersections: Points where the function crosses the x and y axes.
Monotonicity: Intervals where the function is increasing or decreasing.
Extrema: Maximum and minimum points of the function.
Concavity: Regions where the function is concave up or down.
Inflection points: Where the concavity of the function changes.

Example: For a given function, the domain is (-∞, 3) ∪ (3, ∞), with a vertical asymptote at x = 3 and a horizontal asymptote at y = 5.

Highlight: Understanding these properties is crucial for sketching accurate graphs of functions and solving ejercicios de funciones 3o ESO.

Page 4: Function Transformations and Piecewise Functions

This page covers two important topics:

Function Transformations:

Changing x to -x reflects the function over the y-axis.
Examples are provided for various function types (quadratic, square root, exponential, trigonometric).

Example: For f(x) = x², f(-x) = (-x)² = x², showing that this function is symmetric about the y-axis.

Piecewise Functions:

These are functions defined differently for different intervals of the domain.
The page shows how to analyze and graph piecewise functions.

Highlight: Piecewise functions are important in modeling real-world scenarios where behavior changes at certain points.

This information is valuable for tackling funciones definidas a trozos ejercicios resueltos pdf problems.

Contenido similar

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Knowunity es la app educativa nº 1 en cinco países europeos

Knowunity fue un artículo destacado por Apple y ha ocupado sistemáticamente los primeros puestos en las listas de la tienda de aplicaciones dentro de la categoría de educación en Alemania, Italia, Polonia, Suiza y Reino Unido. Regístrate hoy en Knowunity y ayuda a millones de estudiantes de todo el mundo.

Descargar en

Google Play

Descargar en

App Store

4.9+

valoración media de la app

13 M

A los alumnos les encanta Knowunity

#1

en las listas de aplicaciones educativas de 12 países

950 K+

alumnos han subido contenidos escolares

¿Aún no estás convencido? Mira lo que dicen tus compañeros...

Usuario de iOS

Me encanta esta app [...] ¡¡¡Recomiendo Knowunity a todo el mundo!!! Pasé de un 2 a un 9 con él :D

Javi, usuario de iOS

La app es muy fácil de usar y está muy bien diseñada. Hasta ahora he encontrado todo lo que estaba buscando y he podido aprender mucho de las presentaciones.

Mari, usuario de iOS