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This document contains 7 exercises for a functions test in 3rd year secondary education (ESO). The exercises cover: drawing graphs that do and do not represent functions; analyzing graphs of functions including domain, range, continuity, and extrema; sketching graphs that meet given criteria for domain, intercepts, and extrema; determining equations of lines given points and slopes; finding the slope and y-intercept of a given line; sketching the graph of a polynomial function; and sketching the graph of a piecewise defined function.
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![FUNCTIONS TEST - 3º ESO
Exercise 1: (0.5 points) Draw a graph that doesn't represent a function. Why?
Exercise 2: (1.75 points) Given the following graph of a certain function:
a) Indicate its domain and its image. Is it a continuous function? Why?
b) Determine the points where the function crosses the axes
c) Study its monotony
d) Study the local and global extrema
Exercise 3: (0.75 points) Work out the graph of a function that fulfills all the following
characteristics at the same time:
a) Its domain is ( 7, 1] [2, )
b) It crosses the axes at the points (-5,0) and (3,0)
c) It has a minimum at x = -3 and a maximum at x=7, either local or global
Exercise 4: (2.25 points)
a) Work out the equation of the straight line that passes through the point A(5, -1) and has
a slope m = -3
b) Work out the equation of the straight line that passes through the points A(-2, 1) and
B(6, 5)
c) Work out the equation of the straight line that is parallel to 6 2 7 0x y and passes
through the point P(2, -5)
Exercise 5: (0.75 points) Indicate the value of the slope of the straight line 5 7 9 0x y ,
and the point where it crosses the y-axis](https://image.slidesharecdn.com/3functions-150305070057-conversion-gate01/85/3functions-1-320.jpg)
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Finlandia invierte fuertemente en educación para toda su población desde la educación básica hasta la educación continua, a pesar de tener pocos recursos naturales. Gracias a esta inversión en capital humano, Finlandia ha logrado construir una economía altamente competitiva e industrializada con bajos niveles de corrupción, al permitir que su pueblo elija dirigentes honestos y competentes a través de un electorado informado.
Zully evaluacion finaal
El documento presenta información sobre diferentes herramientas TIC como Yahoo, redes sociales (Facebook, Instagram, YouTube), Google, PowerPoint, juegos educativos y Audacity. Describe sus usos y ventajas como medios de investigación, comunicación y entretenimiento, pero también señala posibles desventajas como el uso inadecuado o la creación de dependencia.
Camtasia
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Libraries Leading the Way on the 'Textbook Problem'
Libraries are taking a leading role in addressing the high cost of textbooks by developing expertise in alternative textbook models. They are advocating for affordable options, educating faculty on alternatives, and directly supporting the creation and hosting of open educational resources. Some libraries purchase one copy of each required textbook and partner with bookstores. However, they are now putting more effort into transforming the textbook market by licensing and hosting open textbooks online, providing print-on-demand options, and working with companies developing new affordable textbook models.
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A2 Reccy Document
Jamie Mears is filming a music video at The Blandford School that will include both performance and narrative sections. The filming will take place in a drama studio and around the school grounds. Lighting equipment will need to be brought in as most locations rely on sunlight, which won't provide consistent lighting for the video.
Mate5 final
Este documento presenta la introducción y los créditos de un cuaderno de matemáticas para 5to grado. Explica que el cuaderno fue producido por el Ministerio de Educación de Argentina para acompañar el trabajo docente y garantizar el acceso a los conocimientos priorizados. El objetivo es promover el diálogo pedagógico y contribuir a construir una educación que promueva la igualdad y el futuro de los estudiantes.
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Similar to 3functions
April 13, 2015
This document contains information about a math class that is reviewing quadratic functions. It includes:
1. An outline of the class agenda which focuses on reviewing key concepts like how the b-value affects the parabola and completing classwork.
2. Details about grading which includes assignments, homework, tests, the final exam, and notebook checks.
3. Sample problems and class notes focused on quadratic functions, including the axis of symmetry, vertex, graphing techniques, and how changing a, b, and c values impacts the parabola.
4. Examples of completing the steps to graph quadratic functions like plotting points and reflecting over the axis of symmetry.
Chapter 5 Point Slope Form
The document provides examples and explanations for writing linear equations in point-slope and slope-intercept form given the slope and a point, or two points on the line. It includes warm-up questions, examples with step-by-step solutions for writing equations from graphical and numerical information, and a problem applying the concepts to a real-world situation. Practice problems assess understanding of writing linear equations from geometric or tabular data.
Save and Submit Q U E S T I O N 1 Use the given c.docx
Save and Submit
Q U E S T I O N 1
Use the given conditions to write an equation for the line in point-
slope form.
Slope = 4, passing through (-3, 7)
A. x - 7 = 4(y + 3)
B. y = 4x - 19
C. y - 7 = 4(x + 3)
D. y + 7 = 4(x - 3)
5 points
Q U E S T I O N 2
Use the given conditions to write an equation for the line in point-
slope form.
Slope = , passing through (8, 7)
A.
y + 7 = (x + 8)
B.
x - 7 = (y - 8)
C.
y = x + 8
D.
y - 7 = (x - 8)
5 points
Q U E S T I O N 3
Determine whether the relation is a function.
{(-2, -7), (3, -5), (6, -4), (9, -6), (10, -1)}
A. Function
B. Not a function
5 points
Q U E S T I O N 4
Find the slope of the line that goes through the given points.
(-1, 4), (5, 4)
A. 2
B. Undefined
C. 0
D.
5 points
Q U E S T I O N 5
Determine whether the equation defines y as a function of x.
x
2
+ y
2
= 1
A. y is a function of x
B. y is not a function of x
5 points
Q U E S T I O N 6
Determine whether the relation is a function.
{(-6, -9), (-2, 1), (1, -1), (7, -7)}
A. Not a function
B. Function
5 points
Q U E S T I O N 7
Determine whether the equation defines y as a function of x.
x = y
2
A. y is not a function of x
B. y is a function of x
5 points
Q U E S T I O N 8
Determine whether the relation is a function.
{(1, -3), (1, 1), (6, -8), (9, -3), (11, -3)}
A. Not a function
B. Function
5 points
Q U E S T I O N 9
Find the slope of the line that goes through the given points.
(-8, 8), (-5, 2)
A. - 2
B.
C.
-
D.
5 points
Q U E S T I O N 1 0
Find the slope of the line that goes through the given points.
(-2, -6), (-9, -17)
A.
-
B.
C.
D.
5 points
Q U E S T I O N 1 1
Find the slope of the line that goes through the given points.
(-3, -7), (9, -7)
A. 1
B. 0
C. -4
D. 4
5 points
Q U E S T I O N 1 2
Evaluate the function at the given value of the independent variable
and simplify.
f(x) = 4x
2
+ 5x - 6; f(x - 1)
A. 4x
2
- 3x - 7
B. 4x
2
- 19x + 3
C. -3x
2
+ 4x - 7
D. 4x
2
- 3x + 3
5 points
Q U E S T I O N 1 3
Determine whether the relation is a function.
{(-5, -4), (-2, 9), (-1, -2), (-1, 7)}
A. Function
B. Not a function
5 points
Q U E S T I O N 1 4
Evaluate the function at the given value of the independent variable
and simplify.
f(x) = -3x - 8; f(-2)
A. -11
B. -2
C. 22
D. 14
5 points
Q U E S T I O N 1 5
Evaluate the function at the given value of the independent variable
and simplify.
f(x) = ; f(5)
A.
B.
C.
D.
5 points
Q U E S T I O N 1 6
Find the slope of the line that goes through the given points.
(3, -5), (-9, -8)
A.
B. 4
C.
-
D.
5 points
Q U E S T I O N 1 7
Evaluate .
Find the slope-intercept form of the equation of the line that pas.docx
Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m. Sketch the line.
A.
y=7x+7
B.
y=7x-4
C.
y=7x+7
D.
y=-4x-4
E.
y=7x-7
5 points
QUESTION 2
Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.
(-6,6), m=-2
A.
y=6x+6
B.
y=6x-6
C.
y=-6x-6
D.
y=-2x-6
E.
y=-2x+6
5 points
QUESTION 3
Determine whether the lines are parallel, perpendicular, or neither.
A.
Parallel
B.
Perpendicular
C.
Neither
5 points
QUESTION 4
Evaluate the function ƒ(x) = 6x - 5 at ƒ(1)
A.
2
B.
1
C.
-1
D.
0
E.
3
5 points
QUESTION 5
A.
8
B.
25
C.
9
D.
-25
E.
8
5 points
QUESTION 6
Does the table describe a function?
A.
no
B.
yes
5 points
QUESTION 7
A.
-h - 8, h≠0
B.
-h - 6, h≠0
C.
-h - 5, h≠0
D.
-h - 9, h≠0
E.
-h - 7, h≠0
5 points
QUESTION 8
Find all real values of x such that ƒ(x) = 0.
ƒ(x) = 42 - 6x
A.
7
B.
5
C.
9
D.
6
E.
8
5 points
QUESTION 9
Find all real values of x such that ƒ(x) = 0
A.
5/4
B.
1
C.
9/8
D.
7/8
E.
11/8
5 points
QUESTION 10
Find the domain of the function.
A.
All real numbers t except t≠0
B.
Negative real numbers t
C.
All real numbers t such that t > 0
D.
Non-negative real numbers t
E.
All real numbers t such that t<0
5 points
QUESTION 11
Find the average rate of change of the function from x1=0 to x2=3
ƒ(x) = 7x + 13
A.
The average rate of change from x1=0 to x2=3 is -7
B.
The average rate of change from x1=0 to x2=3 is 7
C.
The average rate of change from x1=0 to x2=3 is -13
D.
The average rate of change from x1=0 to x2=3 is 13
E.
The average rate of change from x1=0 to x2=3 is 19
5 points
QUESTION 12
Find the zeroes of the function algebraically.
ƒ(x) = 2x2 - 3x - 20
A.
-5/2, 4
B.
-5/2, -4
C.
-2/5, 4
D.
5/2, -4
E.
5/2, 4
5 points
QUESTION 13
Find (ƒ+g)(x)
ƒ(x) = x+3, g(x) = x - 3
A.
2x
B.
3x
C.
-3x
D.
-2x
E.
2x+6
5 points
QUESTION 14
Find (ƒ-g)(x)
ƒ(x) = x + 6, g(x) = x - 6
A.
2x - 12
B.
12
C.
2x - 6
D.
2x + 12
E.
2x
5 points
QUESTION 15
Find (ƒg)(x)
ƒ(x) = x2, g(x) = 7x - 6
A.
7x3 + 6x2
B.
7x3 - 6x2
C.
7x2 - 6x3
D.
7x2 + 6x3
E.
7x - 6x2
5 points
QUESTION 16
Evaluate the indicated function for ƒ(x) = x2 + 3, g(x) = x - 5
(ƒ + g)(6)
A.
42
B.
-40
C.
34
D.
44
E.
40
5 points
QUESTION 17
find ƒ ∘ g
ƒ(x) = x2, g(x) = x - 5
A.
x2
B.
(x-5)2
C.
(x+5)2
D.
x2-5
E.
x2+5
5 points
QUESTION 18
Find the slope and y-intercept (if possible) of the equation of the line. Sketch the line.
y = 7x + 5
A.
m = 7
y-intercept (0,5)
B.
m = -7
y-intercept: (0,5)
C.
m=5
y-intercept: (0,5)
D.
m = -5
y-intercept: (0,5)
E.
m is undefined
y-intercept: (0,5)
5 points
QUESTION 19
Plot the points and find the slope of the line passing through the pair of points
(0,6), (4,0)
A.
m = 3/4
B.
m = -3/2
C.
m = -3/2
D.
m = -2/3
E.
m = 3/2
5 points
QUESTION 20
Plot the points and find the lope of th ...
April 10, 2015
The document discusses graphing quadratic functions. It begins with reviewing key concepts like the vertex and axis of symmetry. The effects of the a, b, and c coefficients on the parabola are explained. Examples are provided to show how changing these values affects the width, direction opened, and vertical translation of the graph. The class will graph various quadratic functions by finding the axis of symmetry, vertex, y-intercept, and other points to plot the parabola. Students are assigned class work problems to graph quadratic functions and show their work.
April 9, 2015
The document discusses graphing quadratic functions. It begins with reviewing key concepts like the vertex and axis of symmetry and how the a, b, and c coefficients affect the graph. Examples are provided for determining the width, direction opened, and vertical shift based on these coefficients. The remainder of the document provides step-by-step examples of graphing quadratic functions by finding the axis of symmetry, vertex, y-intercept, and other points to plot the parabolic curve.
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Here are the steps to solve this problem numerically in MATLAB:
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y2' = -sin(y1)
2. Create an M-file function pendulum.m that returns the right hand side:
function dy = pendulum(t,y)
dy = [y(2); -sin(y(1))];
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This document provides an introduction to using MATLAB for image processing. It discusses how images are represented as matrices in MATLAB and how various MATLAB functions and operators can be applied to images. It covers importing and exporting different image formats, performing arithmetic operations on images, using logical conditions to extract pixel values, different methods of image display, and writing M-files to define image processing functions. The key concepts of linear systems, superposition, impulse response, convolution, and correlation are also introduced in the context of digital signal and image processing applications in MATLAB.
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The document discusses different types of modeling involving functions. It provides examples of exponential, logarithmic, and circular functions where the variables or constants are missing and points on the graphs are given. Readers are instructed to find the values of the missing variables or constants by inserting the points into the corresponding function equations. Exercises from the textbook are assigned for practice.
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This document contains instructions and questions for a college algebra written assignment. It asks the student to answer multiple choice and free response questions related to topics covered in the textbook, including graphing functions, solving equations and inequalities, working with lines and systems of equations. The student is to show all work and refer to graphs in the textbook to answer some questions. The assignment is divided into sections covering various algebra concepts.
Module 1 linear functions
This module introduces linear functions. It defines a linear function as one that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. It explains how to graph linear functions given two points, the x- and y-intercepts, the slope and a point, or the slope and y-intercept. The document provides examples and practice problems for students to learn how to represent linear functions in different forms, rewrite them between standard and slope-intercept form, and graph them based on given information.
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1. The document provides information on linear functions and how to determine if an equation represents a linear function. It discusses using standard form (Ax + By = C) to identify linear equations and determine intercepts.
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Chapter 1 MATLAB Fundamentals easy .pptx
MATLAB can be used for calculation, plotting, image processing, and modeling. It allows defining variables and performing operations on vectors, arrays, and matrices. Key functions include plotting graphs, solving equations, performing calculus operations like derivatives and integrals, and applying built-in functions to arrays.
Apoyo guía-12-2°-medio-ppt.-parábola
This document discusses the key elements of a quadratic function f(x) = ax^2 + bx + c. It explains that:
1) The y-intercept is indicated by the c coefficient as (0,c)
2) The vertex is calculated as (-b/2a, f(-b/2a))
3) The axis of symmetry passes through the vertex and is the line x=-b/2a.
It provides an example of the quadratic function f(x)=x^2+2x-8 and graphs it to illustrate these elements.
Đề Thi HK2 Toán 7 - THCS Hermann Gmeiner
The document contains 6 math problems from a 7th grade test in Vietnam.
Problem 1 involves creating a frequency table and calculating the mean from data on test scores.
Problem 2 asks for the length of a ladder needed where the base is 1m from the bottom of a 4m pipe.
Problem 3 involves simplifying an algebraic expression and evaluating it for given values.
Problems 4-6 involve polynomial expressions, solving equations, and proving properties of triangles.
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This document contains a practice exam for Math 220 with 16 multi-part questions covering topics such as functions, inequalities, trigonometry, logarithms, and graphing. The exam instructs students to show their work to receive partial credit and enough work to receive full credit. It tests skills like finding domains of functions, solving inequalities, determining equations of lines and circles, properties of functions, evaluating trigonometric and logarithmic expressions, solving equations, and graphing functions.
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This document provides a module on linear functions. It defines linear functions as those that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. The module teaches how to determine if a function is linear, rewrite linear equations in slope-intercept form, and graph linear functions given various inputs like two points, x- and y-intercepts, slope and a point, or slope and y-intercept. Examples and practice problems are provided to help students learn to identify, write, and graph different types of linear functions.
Math 223 Disclaimer It is not a good idea.docx
Math 223
Disclaimer:
It is not a good idea to rely exclusively on reading through old exam solutions as a
way to prepare for the final exam. In particular, this semester's course director
may not have written any of the exams available from this page, so the ones he/she
gives will almost certainly have a somewhat different flavor.
Topic Warning:
Because the topics taught differ slightly from semester to semester, it is not a good
idea to use the old exams to gauge the content of the exams this semester.
Math 223 Show Your Work! Page 1 of 11
1. (8) Consider two vectors
#„v = 4
#„
i �
#„
j + a
#„
k and #„w = a
#„
i + 5
#„
j �
#„
k . For what values of
a are #„v and #„w perpendicular?
2. (8) Find an equation for the plane passing through the points
(0, 2, 1), (1, 1, 5), and (2, 0, 11).
3. (8) Find a vector of magnitude 10 normal to the plane 5x + 3y = 6z + 1.
Math 223 Show Your Work! Page 2 of 11
4. (8) At which point (or points) on the ellipsoid x2 + 4y2 + z2 = 9 is the tangent plane
parallel to the plane z = 0?
5. (8) Find a parametric equation for a line through the point (1, �3, 5) and parallel to the
vector 5
#„
i + 3
#„
j �
#„
k
Math 223 Show Your Work! Page 3 of 11
6. (8) Find the directional derivative of f(x, y) = x2y + y2x at the point (1, �1) in the
direction of 3
#„
i � 4
#„
j .
7. (7) Compute the flux integral
Z
S
#„
F ·
# „
dA where
#„
F =
#„
i +
#„
j �
#„
k and S is the surface
z = x2 � y2, 0 x 3, 0 y 3, oriented upwards.
Math 223 Show Your Work! Page 4 of 11
8. (20) Consider the integral
Z 1
0
Z 2
(8y)1/3
1
1 + x4
dxdy.
(a) Interchange the order of integration. Show your work by including a sketch of the
region of integration.
(b) Evaluate the integral.
Math 223 Show Your Work! Page 5 of 11
9. (20) Let
#„
F = x
#„
i + y
#„
j + z
#„
k . Evaluate the following:
(a)
Z
C
#„
F ·
#„
dr where C is the line from (0, 0, 0) to (1, 1, 1).
(b)
Z
S
#„
F ·
# „
dA where S is the triangle in the plane y = 10 with vertices (0, 10, 0), (4, 10, 0),
and (0, 10, 1), oriented in the direction of increasing y.
(c)
Z
S
#„
F ·
# „
dA where S is the sphere of radius 2 centered at (5, 5, 0), oriented outward.
Math 223 Show Your Work! Page 6 of 11
10. (15) Let H(x, y, z) = sin (2x + y) + z. Find the equation of the tangent plane to the
level surface H(x, y, z) = 5 at the point (⇡, ⇡, 5).
Math 223 Show Your Work! Page 7 of 11
11. (20) Let
#„
F = (y + z)x
#„
i + y
#„
j + xyz
#„
k .
(a) Find curl(
#„
F ).
(b) Let S be the surface x2 + y2 + z = 25, with 0 z 25, oriented upward. Find the
value of the flux integral
Z
S
curl(
#„
F ) ·
# „
dA.
Math 223 Show Your Work! Page 8 of 11
12. (15) Let a be a constant, a 6= 2, and consider function f(x, y) =
1
2
x2 + 2y + 2xy + ay2.
(a) Find the critical point of f.
(b) Find all values of a so that the critical point is a global minimum.
Math 223 Show Your Work! Page 9 of 11
13. (20) C ...
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
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Chapter 4
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Chapter 5
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Chapter 6
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Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
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Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
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Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Training: ISO/IEC 27001 Information Security Management System - EN | PECB
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