For the polynomial function f(x) = -3x^5 + 2x^2 - 7 , what is the end behavior of the graph as x approach positive and negative infinity?

As x \to \infty, f(x) \to -\infty and as x \to -\infty, f(x) \to \infty

As x \to \infty, f(x) \to \infty and as x \to -\infty, f(x) \to -\infty

As x \to \infty, f(x) \to -\infty and as x \to -\infty, f(x) \to -\infty

As x \to \infty, f(x) \to \infty and as x \to -\infty, f(x) \to \infty

Which of the following describes the end behavior of the polynomial function p(x) = 4x^4 - 5x^3 + x - 10 ?

The graph rises to the left and rises to the right.

The graph falls to the left and rises to the right.

The graph falls to the left and falls to the right.

The graph rises to the left and falls to the right.

If a polynomial function f(x) has a leading term of -2x^6 , which statement correctly describes its end behavior?

As x \to \infty, f(x) \to -\infty and as x \to -\infty, f(x) \to -\infty

As x \to \infty, f(x) \to \infty and as x \to -\infty, f(x) \to \infty

As x \to \infty, f(x) \to \infty and as x \to -\infty, f(x) \to -\infty

As x \to \infty, f(x) \to -\infty and as x \to -\infty, f(x) \to \infty

Identify the end behavior of the polynomial function f(x) = -2x^2(x - 3)(x + 4) .

As x \to \infty, f(x) \to -\infty and as x \to -\infty, f(x) \to -\infty

As x \to \infty, f(x) \to -\infty and as x \to -\infty, f(x) \to \infty

As x \to \infty, f(x) \to \infty and as x \to -\infty, f(x) \to -\infty

As x \to \infty, f(x) \to \infty and as x \to -\infty, f(x) \to \infty

What is the end behavior of the polynomial function f(x) = (1 - x)(x + 2)(x - 3) ?

As x \to \infty, f(x) \to -\infty and as x \to -\infty, f(x) \to \infty

As x \to \infty, f(x) \to \infty and as x \to -\infty, f(x) \to \infty

As x \to \infty, f(x) \to \infty and as x \to -\infty, f(x) \to -\infty

As x \to \infty, f(x) \to -\infty and as x \to -\infty, f(x) \to -\infty

End behavior of Polynomial Functions

Here is a quiz based on the “Reciprocal of a Linear Function” content from your PowerPoint. --- Quiz: Reciprocal of a Linear Function Multiple Choice (5 questions) Select the best answer. 1. What is the vertical asymptote of f(x) = \dfrac{1}{x - 3}? a) x = 0 b) x = 3 c) x = -3 d) y = 0 2. For f(x) = \dfrac{1}{2x + 4}, what is the y-intercept? a) 0 b) \dfrac{1}{2} c) \dfrac{1}{4} d) 2 3. What is the horizontal asymptote of any function of the form f(x) = \dfrac{1}{ax + b} (with a \neq 0)? a) y = 0 b) y = 1 c) x = 0 d) x = -\dfrac{b}{a} 4. The domain of f(x) = \dfrac{1}{5 - x} is a) all real numbers except 5 b) all real numbers except -5 c) all real numbers d) all real numbers except 0 5. As x approaches the vertical asymptote from the right, the values of f(x) a) approach 0 b) approach \pm\infty c) approach 1 d) approach the same value as from the left --- Completion (5 questions) Fill in the blank with the correct word or expression. 1. The vertical asymptote of a reciprocal linear function occurs where the ____________________ is zero. 2. The horizontal asymptote of f(x) = \dfrac{1}{ax + b} is the line y = ________. 3. A function of the form f(x) = \dfrac{1}{ax + b} has ______ x-intercept(s) because the numerator is constant. 4. The end behavior of f(x) = \dfrac{1}{x - 2} as x \to \infty is f(x) \to ________. 5. The y-intercept of f(x) = \dfrac{1}{3x - 6} is ________. --- Answer Key Multiple Choice 1. b) x = 3 2. c) \dfrac{1}{4} (Substitute x = 0: f(0) = \frac{1}{4}) 3. a) y = 0 4. a) all real numbers except 5 5. b) approach \pm\infty Completion 6. denominator 7. 0 8. no / zero 9. 0 (from the positive side) 10. -\dfrac{1}{6} (Substitute x = 0: f(0) = \frac{1}{-6})

REMAINDER THEOREM, FACTOR THEOREM, RULES OF SIGNS ,RATIONAL ROOTS THEOREM AND END BEHAVIOR

Can you make a multiple choice of test questions regarding this information given which is Curriculum from Different Points of View There are many definitions of curriculum. Because of this, the concept of curriculum is sometimes characterized as fragmentary, elusive and confusing. However, the numerous definitions indicate dynamism that connotes diverse interpretations of what curriculum is all about. The definitions are influenced by models of thought, pedagogies, political as well as cultural experiences. Let us study some of these definitions. 1. Traditional Points of View of Curriculum In early years of the 20th century, the traditional concepts held of the “curriculum is that it is a body of subjects or subject matter prepaid by the teachers for the student’s to learn”. It was synonymous to the “course of study” and “syllabus” Robert M. Hutchins views curriculum as “permanent studies” where the rules of grammar, reading, rhetoric and logic and mathematics for basic education are emphasized. Basic education should emphasize the 3 Rs and college education should be grounded on liberal education. On the other, Arthur Bestor as an essentialist, believes that the mission of the school should be intellectual training, hence curriculum should focus on the fundamental intellectual disciplines of grammar, literature and writing. It should also include mathematics, science, history and foreign language. The definition leads us to the view of Joseph Schwab that discipline is the sole source of curriculum. Thus in our education system, curriculum is divided into chunks of knowledge we call subject areas in basic education such as English, Mathematics, Science, Social Studies and others. In college, discipline may include humanities, sciences, language and many more. To Phoenix, curriculum should consist entirely of knowledge which comes from various disciplines. Academic discipline became the view of what curriculum is after the cold war and the race to space. Joseph Schwab, a leading curriculum theorist coined the term discipline as a ruling doctrine for curriculum development. Curriculum should consist only of knowledge which comes from disciplines which is the sole source. Thus curriculum can be viewed as a field of study. It is made up of its foundations (philosophical, historical, psychological and social foundations); domains of knowledge as well as its research theories and principles. Curriculum is taken as scholarly and theoretical. It is concerned with broad historical, philosophical and social issues and academics. Most of the traditional ideas view curriculum as written documents or a plan of action in accomplishing goals. 2. Progressive Points of View of Curriculum On the other hand, to a progressivist, a listing of school subjects, syllabi, course of study, and a list of courses or specific discipline do not make a curriculum. These can only be called curriculum if the written materials are actualized by the learner. Broadly speaking, curriculum is defined as the total learning experiences of the individual. This definition is anchored on John Dewey’s definition of experience and education. He believed that reflective thinking is a means that unifies curricular elements. Thought is not derived from action but tested by application. Caswell and Campbell viewed curriculum as “all experiences children have under the guidance of teachers”. This definition is shared by Smith, Stanley and Shores when they defined “curriculum as a sequence of potential experiences set up in the schools for the purpose of disciplining children and youth in group ways of thinking and acting”. Marsh and Willis on the other hand view curriculum as all the “experiences in the classroom which are planned and enacted by the teacher, and also learned by the students”. Points of View on Curriculum Development From the various definitions and concepts presented, it is clear that curriculum is a dynamic process. Development connotes changes which are systematic. A change for the better means any alteration, modification or improvement of existing condition. To produce positive changes, development should be purposeful, planned and progressive. This is how curriculum evolves. Let us look at the two models of curriculum development and concepts of Ralph Tyler and Hilda Taba. Ralph Tyler Model: Four Basic Principles. This is also popularly known as Tyler’s Rationale. He posited four fundamental questions or principles in examining any curriculum in schools. These four fundamental principles are as follows: 1. What educational purposes should the school seek to attain? 2. What educational experiences can be provided that are likely to attain these purposes? 3. How can these educational experiences be effectively organized? 4. How can we determine whether these purposes are being attained or not? In summary, Tyler’s Model show that in curriculum development, the following considerations should be made: (1) Purpose of the school, (2) Educational experiences related to the purposes, (3) Organization of the experiences, and (4) Evaluation of the experiences. On the other hand, Hilda Taba improved on Tyler’s Rationale by making a linear model. She believed that teachers who teach or implement the curriculum should participate in developing it. Her advocacy was commonly called the grassroots approach. She presented seven major steps to her model where teachers could have a major input. These steps are as follows: 1. Diagnosis of learner’s needs and expectations of the larger society. 2. Formulation of learning objectives. 3. Selection of learning content. 4. Organization of learning content. 5. Selection of learning experiences. 6. Organization of learning activities. 7. Determination of what to evaluate and the means of doing it. Thus as you look into curriculum models, the three interacting processes in curriculum development are planning, implementing and evaluating. Types of Curriculum Operating in Schools From the various concepts given, Allan Glatthorn(2000) describes seven types of curriculum operating in the schools. These are (1) Recommended curriculum- proposed by scholars and professional organizations. (2) Written Curriculum- appears in school, district, division or country documents. (3) Taught Curriculum- what teacher’s implement or deliver in the classrooms and schools. (4) Supported Curriculum- resources-textbooks, computers, audio- visual materials which support and help in the implementation of the curriculum. (5) Assessed Curriculum- that which is tested and evaluated. (6) Learned Curriculum- which the students actually learn and what is measured and (7) Hidden Curriculum- the unintended curriculum. 1. Recommended Curriculum- Most of the school curricula are recommended. The curriculum may come from a national agency like the Department of Education, Commission on Higher Education (CHED), Department of Science and Technology (DOST) or any professional organization who has stake in education. For example the Philippine Association for Teacher Education (PAFTE) or the Biology Teacher Association (BIOTA) may recommend a curriculum to be implemented in the elementary or secondary education. 2. Written Curriculum- This includes documents, course of study or syllabi handed down to the schools, districts, division, departments or colleges for implementation. Most of the written curricula are made by curriculum experts with participation of teachers. These were pilot-tested or tried out in sample schools or population. Example of this is the Basic Education Curriculum (BEC). Another example is the written lesson plan of each classroom teacher made up of objectives and planned activities of the teacher. 3. Taught Curriculum- The different planned activities which are put into action in the classroom compose the taught curriculum. These are varied activities that are implemented in order to arrive at the objectives or purposes of the written curriculum. These are used by the learners with the guidance of teachers. Taught curriculum varies according to the learning styles of students and the teaching styles of teachers. 4. Supported Curriculum- In order to have a successful teaching, other than the teacher, there must be materials which should support or help in the implementation of a written curriculum. These refer to the support curriculum that includes material resources such as textbooks, computers, audio-visual materials, laboratory equipment, playgrounds, zoos and other facilities. Support curriculum should enable each learner to achieve real and lifelong learning. 5. Assessed Curriculum- This refers to a tested or evaluated curriculum. At the duration and end of the teaching episodes, series of evaluations are being done by the teachers to determine the extent of teaching or to tell if the students are progressing. This refers to the assessed curriculum. Assessment tools like pencil-and-paper tests, authentic instruments like portfolio are being utilized. 6. Learned Curriculum- This refers the learning outcomes achieved by the students. Learning outcomes are indicated by the results of the tests and changes in behavior which can either be cognitive, affective or psychomotor. 7. Hidden Curriculum- This is the unintended curriculum which is not deliberately planned but may modify behavior or influenced learning outcomes. There are lots of hidden curricula that transpire in the schools. Peer influence, school environment, physical condition, teacher-learner interaction, mood of the teachers and many other factors made up the hidden curriculum.

You have recently re-evaluated John, a 16-year-old high school student who has been identified as having a learning disability. John has been exhibiting behavior concerns in high school, including insubordination towards staff, and fighting with students; he has been suspended for six days so far in the school year. You had interviewed him about his behavior using informal questions. Because you have known John several years (he went to your assigned elementary school), you have established a strong rapport with him. John was agitated the day you worked with him because his friend had been hospitalized for a drug overdose over the weekend. He was very critical of some students and said staff favored this group over everyone. He also shared with you some confidential information about the friend and other friends of his who are using drugs. John admitted to you confidentially that he has experimented with drugs but he is not using; the concern he has for his friend seems sincere in that he doesn’t want to end up the same way. The principal comes to you and requests that you look at a higher level of placement for John, as he has just been suspended again for fighting. He specifically requests that you share the assessment data you have collected. Ethical Decision Making Model: § Describe the problem situation: § Define the potential ethical – legal issues involved: § Consult available ethical and legal guidelines: § Consult with supervisors and colleagues: § Evaluate the rights, responsibilities, and welfare of all affected parties: § Consider alternative solutions and consequences of making each decision:  Make the decision:  Questions to consider: § What information could you share in keeping with the assessment ethics? § Taking into account the NASP ethics on relationships and confidentiality (refer to information from previous courses as well), what decision do you think you would make?

You have recently re-evaluated John, a 16-year-old high school student who has been identified as having a learning disability. John has been exhibiting behavior concerns in high school, including insubordination towards staff, and fighting with students; he has been suspended for six days so far in the school year. You had interviewed him about his behavior using informal questions. Because you have known John several years (he went to your assigned elementary school), you have established a strong rapport with him. John was agitated the day you worked with him because his friend had been hospitalized for a drug overdose over the weekend. He was very critical of some students and said staff favored this group over everyone. He also shared with you some confidential information about the friend and other friends of his who are using drugs. John admitted to you confidentially that he has experimented with drugs but he is not using; the concern he has for his friend seems sincere in that he doesn’t want to end up the same way. The principal comes to you and requests that you look at a higher level of placement for John, as he has just been suspended again for fighting. He specifically requests that you share the assessment data you have collected.

Measuring the Effectiveness of police strategies and operations Clearance rates Def: The proportion of incidents known to the police that result in teh identification of a suspect Crime Displacement Def: relocation-due to the effective crime prevention, crime response initiates criminal activity from one local to another Professional Model of Policing Model of police work, reactive, incident driven and centred on random patrol Three Rs: random patrol, rapid response and reactive investigation Community policing Def: policing centred on police-community partnership and problem-solving The three ps: prevention, problem solving and partnership with the proactive role Community-based strategic policing Def: The model incorporates community policing with prevention, crime response and crime attack approaches Community engagement, police services strategic in their policies and operations Crime Analytics Sophisticated programs, and crime maps, provide intelligence to police officers in patrol and investigative units Intelligence-led policing: guided by collection, and analysis of information informs police decision-making Compstat: Increase effectiveness, and efficiency of police service while holding police personnel accountable for crime reduction Predictive policing: statistical analysis, identify time and location likely to occur Limited analytical capacity and not able to provide their officers with real-time information Biased policing certain areas, or persons, being identified as important for police attention in predictive policing How Predictive Policing Software Works The Police and the community Public Attitudes toward and Confidence in the police Community-based strategic policing: Recruitment, and deployment of volunteers in community police stations, storefronts Foot and bike patrols Team policing Restorative Justice Approaches Alternative for addressing, and resolving crime, needs of victims, offenders and the community Victim offender meditation Circle sentencing Community holistic healing programss Family group conferences Crime Prevention and Response Strategies Crime Prevention progemas Aimed at reducing crime, generating community involvement and heightening citizens; perceptions of safety Primary crime prevention programs opportunities for criminal offences and alter those conditions Secondary crime prevention programs focus on areas that produce crime and disorder Tertiary crime prevention programs are designed to prevent youth and adults from reoffending The Broken Windows Approach If minor crimes are left unaddressed in an environment, more serious crimes will emerge (originated in New York City in the 1980’s) “The exictsnce of unchecked and uncontrolled mirror incivilites in a neighbourhood- for example, panhandling, public drunkenness, vandalism and graffiti-produces an atmosphere conducive to more serious crime.” R.H. Burke Zero tolerance policing Zero tolerance policing: Strict order maintenance approach- specific area, coupled with high police visibility and presence Quality of life policing: Increased police visibility improves conditions in an area by targeting disruptive and annoying behaviour Problem Oritented policing (POP) Strategy, the idea that police should address teh cause of recurrent crime and disorder Root causes of recurring problems Solutions to problems Collabortaion with community SARA (scanning, analysis, response and assessment) problem-solving model helps officers identify, and respond to problems with the assistance of agencies, organizations, community groups The Police and Vulnerable/ At risk groups Persons with Mental Illness Patrol officers encountering more and more persons with mental illness (PwMi) Number of these end trragically Number of incidents increased significantly following deinstitutionalization of the mentally ill - in 1960 and 1970 De facto (in fact) mental health workers, first responders Crisis intervention training (CIT) Assertive outreach teams Assertive community treatment (ACT) teams Indigenouse, Vulnerable, and Marginalized women Sexual assault one of most underreported crimed. 1 in 20 incidents report to police. Many Women Do not want to deal with police Believe police would not take allegation seriously Language, cultural barriers Distrust the police Fear repercussions Missing and Murdered Indigenous women Canada, unknown number of missing and murdered indigenous women 2016, federal government announced National inquiry into Missing and Murdered Indigennouse women and girls Three goals of MMIWG 1. Finding the truth 2. Honouring the truth 3. Giving life to the truth as a path of healing

Related quizzes

Related quizzes