Precalculus -- Functions and Graphs

Precalculus -- Functions and Graphs


Fall 2012
08/27/2012 - 12/16/2012

Course Information

Section 012
MW 09:00 - 10:45
PIN1 612
Aly Yahya

Office Hours

No office hours have been entered for this term

Course Requirements


MATH 2412 PRECALCULUS: FUNCTIONS AND GRAPHS (4-4-0).This is a course designed to prepare students for MATH 2413 Calculus I. Content includes algebraic, logarithmic, exponential, and trigonometric functions and equations; parametric equations; and the polar coordinate system.


MATH 1316 with a C or better or equivalent. Another option is an appropriate secondary school course (one semester of trigonometry or precalculus or the equivalent, including trigonometry) and a satisfactory entrance score on the ACC Mathematics Assessment Test.
Importance of Prerequisites: This is not a review course.  If you do not have current knowledge of the material in our MATH 1314 College Algebra, and MATH 1316, Trigonometry, please  ask your instructor about changing to one of these course to better prepare for MATH 2412.


Required Text
Functions Modeling Change: A Preparation for Calculus,  
by Connally, Hughes-Hallet, Gleason, et al., 4th  edition. ISBN: 9780470484753



This course is taught in the classroom primarily as a lecture/discussion course.

Use of Graphing Utilities 
As with any course where either graphing or scientific calculators are used, the calculator will be used as a supportive tool. This course is not about calculator usage, but about precalculus concepts.  We will use graphing calculators when their use enhances the understanding of a mathematical idea.  Graphing calculators are not required for this course. However, as you progress through the semester you may find it convenient to purchase your own.

Course Rationale
This course is designed to teach students the algebraic and trigonometric modeling concepts needed for scientific/engineering calculus. It is not simply a review of college algebra and trigonometry.

Course Subjects

Tests  : Four exams throughout the semester. All administered in class.

           All tests will be administered in class.
            Tests are open answer questions, there won’t be multiple choice questions.
            Notes/cheat sheets are not allowed. Calculators are allowed.


The last page of the syllabus has a list of homework problems that you have to work on and turn in every Monday.
Sections covered on a given week are automatically due the following Monday.

The assignments will be checked for completion however I will randomly check a few problems for accuracy and your grade will be affected accordingly.
Staple your work and make sure to include the section number for each different section.

Late homework will NOT be accepted.
The lowest two homework grades will be dropped.
Get Help Early

It is your responsibility to check your answers on assigned problems and make sure you understand the concepts. You can always ask homework questions at the beginning of class, come to office hours, go to the learning lab or work with classmates.

Determination of Course Grade

Tests average = 85%

HW average = 15%


Grading Scale:

A:  90 – 100

   B:   80 – 89

   C:  70 – 79

  D:  60 – 69

   F:    0 – 59

Missed Exam Policy

If you miss a test, I will let you make it up at the testing center if you provide me with documentation that proves you were unable to come to class on the day of the test (Doctor’s note, police report, etc). If your absence is not justified, you will get a zero on the test you missed. Make up tests are slightly harder. Not being ready for a test is not a valid excuse for taking it later at the testing center, please don’t ask.
No retest allowed.

Attendance/Class Participation
Regular and punctual class attendance is expected of all students.  If attendance or compliance with other course policies is unsatisfactory, the instructor may withdraw students from the class.

Students are expected to participate in class by attending, asking questions, and contributing suggestions and ideas.
Students who have excessive absences (4 or more) may be withdrawn.
Please be courteous.  Disruptive behavior will not be tolerated. Repeat offenders may be withdrawn. All cell phones/pagers must be turned off.


Withdrawal Policy

It is the responsibility of each student to ensure that his or her name is removed from the roll should he or she decide to withdraw from the class.  The instructor does, however, reserve the right to drop a student should he or she feel it is necessary.  If a student decides to withdraw, he or she should also verify that the withdrawal is submitted before the Final Withdrawal Date.  The student is also strongly encouraged to retain their copy of the withdrawal form for their records.

Students who enroll for the third or subsequent time in a course taken since Fall, 2002, may be charged a higher tuition rate, for that course.

State law permits students to withdraw from no more than six courses during their entire undergraduate career at Texas public colleges or universities.  With certain exceptions, all course withdrawals automatically count towards this limit.  Details regarding this policy can be found in the ACC college catalog.

The withdrawal deadline is Monday, November 26, 2012

Reinstatement Policy:

Once withdrawn from the class, a student can only be reinstated in two situations:
 (1) At the student's request, if the student had some documented emergency or tragedy that prevented the student's participation in class for a period of time and had not exceeded six absences or missed any major tests prior to that period of time.
 (2) If the withdrawal was made by instructor or college error. In either case the student is responsible for all missed assignments and must complete remaining assignments and tests on schedule.

Incomplete Grade Policy
An instructor may award a grade of “I” (Incomplete) if a student was unable to complete all of the objectives for the passing grade in a course.  An incomplete grade cannot be carried beyond the established date in the following semester. The completion date is determined by the instructor but may not be later than the final deadline for withdrawal in the subsequent semester.


Course-Specific Support Services

Sometimes sections of MATH 0185 (1-0-2) are offered. The lab is designed for students currently registered in Precalculus MATH 2412. It offers individualized and group setting to provide additional practice and explanation. This course is not for college-level credit. Repeatable up to two credit hours. Students should check the course schedule for possible offerings of the lab class. ACC main campuses have Learning Labs that offer free first-come first-serve tutoring in mathematics courses. The locations, contact information and hours of availability of the Learning Labs are posted at:

Statement on Scholastic Dishonesty
A student attending ACC assumes responsibility for conduct compatible with the mission of the college as an educational institution.  Students have the responsibility to submit coursework that is the result of their own thought, research, or self-expression.  Students must follow all instructions given by faculty or designated college representatives when taking examinations, placement assessments, tests, quizzes, and evaluations.  Actions constituting scholastic dishonesty include, but are not limited to, plagiarism, cheating, fabrication, collusion, and falsifying documents.    Penalties for scholastic dishonesty will depend upon the nature of the violation and may range from lowering a grade on one assignment to an “F” in the course and/or expulsion from the college.  See the Student Standards of Conduct and Disciplinary Process and other policies at

Statement on Scholastic Dishonesty Penalty
Students who violate the rules concerning scholastic dishonesty will be assessed an academic penalty that the instructor determines is in keeping with the seriousness of the offense. This academic penalty may range from a grade penalty on the particular assignment to an overall grade penalty in the course, including possibly an F in the course. ACC's policy can be found in the Student Handbook under Policies and Procedures or on the web at:   

Statement on Student Discipline
Classroom behavior should support and enhance learning. Behavior that disrupts the learning process will be dealt with appropriately, which may include having the

student leave class for the rest of that day. In serious cases, disruptive behavior may lead to a student being withdrawn from the class. ACC's policy on student

discipline can be found in the Student Handbook under Policies and Procedures or on the web at:

Statement on Students with Disabilities
Each ACC campus offers support services for students with documented disabilities.  Students with disabilities who need classroom, academic or other accommodations must request them through the Office for Students with Disabilities (OSD).   Students are encouraged to request accommodations when they register for courses or at least three weeks before the start of the semester, otherwise the provision of accommodations may be delayed.  

Students who have received approval for accommodations from OSD for this course must provide the instructor with the ‘Notice of Approved Accommodations’ from OSD before accommodations will be provided.   Arrangements for academic accommodations can only be made after the instructor receives the ‘Notice of Approved Accommodations’ from the student.  

Students with approved accommodations are encouraged to submit the ‘Notice of Approved Accommodations’ to the instructor at the beginning of the semester because a reasonable amount of time may be needed to prepare and arrange for the accommodations.   

Additional information about the Office for Students with Disabilities is availableat

Statement on Academic Freedom

Institutions of higher education are conducted for the common good. The common good depends upon a search for truth and upon free expression. In this course, the professor and students shall strive to protect free inquiry and the open exchange of facts, ideas, and opinions. Students are free to take exception to views offered in this course and to reserve judgment about debatable issues. Grades will not be affected by personal views.
With this freedom comes the responsibility of civility and a respect for a diversity of ideas and opinions. This means that students must take turns speaking, listen to others speak without interruption, and refrain from name-calling or other personal attacks.

Student And Instructional Services
ACC strives to provide exemplary support to its students and offers a broad variety of opportunities and services.  Information on these services and support systems is available at:

Links to many student services and other information can be found at:

ACC Learning Labs provide free tutoring services to all ACC students currently enrolled in the course to be tutored.  The tutor schedule for each Learning Lab may be found at:

For help setting up your ACCeID, ACC Gmail, or ACC Blackboard, see a Learning LabTechnician at any ACC Learning Lab.



Student Rights and Responsibilities
Students at the college have the rights accorded by the U.S. Constitution to freedom of speech, peaceful assembly, petition, and association. These rights carry with them the responsibility to accord the same rights to others in the college community and not to interfere with or disrupt the educational process. Opportunity for students to examine and question pertinent data and assumptions of a given discipline, guided by the evidence of scholarly research, is appropriate in a learning environment. This concept is accompanied by an equally demanding concept of responsibility on the part of the student. As willing partners in learning, students must comply with college rules and procedures.

Safety Statement

Austin Community College is committed to providing a safe and healthy environment for study and work. You are expected to learn and comply with ACC environmental, health and safety procedures and agree to follow ACC safety policies. Additional information on these can be found at Because some health and safety circumstances are beyond our control, we ask that you become familiar with the Emergency Procedures poster and Campus Safety Plan map in each classroom. Additional information about emergency procedures and how to sign up for ACC Emergency Alerts to be notified in the event of a serious emergency can be found at
Please note, you are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be dismissed from the day’s activity, may be withdrawn from the class, and/or barred from attending future activities. You are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be immediately dismissed from the day’s activity, may be withdrawn from the class, and/or barred from attending future activities. 
Use of ACC email

All College e-mail communication to students will be sent solely to the student’s ACCmail account, with the expectation that such communications will be read in a timely fashion. ACC will send important information and will notify you of any college related emergencies using this account.  Students should only expect to receive email communication from their instructor using this account.  Likewise, students should use their ACCmail account when communicating with instructors and staff.  Instructions for activating an ACCmail account can be found at


Pinnacle testing center location: PIN 706 (7th floor)
Monday - Thursday: 8:00 am - 9:00 pm

Friday:                      8:00 am - 4:00 pm

Closed Saturday and Sunday
Tel: 512-223-8002
ACC Student ID is required to take a test at the testing center.
Do NOT bring cell phones to the Testing Center.  Having your cell phone in the testing room, regardless of whether it is on or off, will revoke your testing privileges for the remainder of the semester.  ACC Testing Center policies can be found at

Prerequisites for Calculus


There are two calculus sequences at ACC (and at most colleges) -- Business Calculus and Calculus. The prerequisite sequence is different for these. Depending on background, students may start the prerequisite sequence at different places.


Intermediate Algebra (MATD 0390)

Intermediate Algebra (MATD 0390)





College Algebra (MATH 1314)



Math for Bus & Eco or (MATH 1324)

College Algebra

(MATH 1314)

Trigonometry (MATH 1316)




Business Calculus I (MATH 1425)

Precalculus (MATH 2412)



Business Calculus II (MATH 1426)

Calculus I (MATH 2413)




Calculus II (MATH 2414)




Calculus III (MATH 2415)





Where to start: The only way that students may skip courses in a sequence is to begin higher in the sequence, based on current knowledge of material from high school courses.
1. A student who needs a review of high school Algebra II will start in Intermediate Algebra (or below.)

2. A student who completed high school Algebra II, but no higher, and whose assessment test score indicates that he/she remembers that algebra, will start in College Algebra or Math for Business & Economics. A substantially higher assessment test score enables the student to start in Trigonometry.

3. A student who completed some precalculus, elementary analysis, or trigonometry in high school, and whose assessment test score indicates that he/she remembers algebra, is eligible to start higher in the sequence than College Algebra. Check the catalog or the math web page.***

* The material in the Trigonometry course requires that students are quite adept with the skills from high school Algebra II (Intermediate Algebra). Some students will achieve that level of skill in the College Algebra course if their placement score is high enough, while others need an additional semester of work on algebra that is done in two courses, Intermediate Algebra and College Algebra.

** Some students who are very successful in College Algebra are tempted to skip either Trigonometry or Precalculus and enroll in Calculus I.
That is not acceptable. Trigonometry topics are essential to success in Calculus, and while it is true that the topic list for Precalculus has only a few additions from the topic list for College Algebra, the level of sophistication of the presentation and the problems on all topics is greater in Precalculus. That increased sophistication is necessary for an adequate background for the Calculus sequence. ***

Notes about the Business sequence: Texas State University requires Math for Business and Economics and Business Calculus I. Students who will attend the UT College of Business must complete the entire Business Calculus sequence before transferring. For more information, including requirements for UT economics students, see

*** For additional information, including prerequisite review sheets for most courses, visit




Student Learning Outcomes/Learning Objectives

Course objectives

  1. Sketch graphs and appropriate transformations for the following: polynomial functions (linear, quadratic, followed by those with degree three and higher), trigonometric functions, exponential and logarithmic functions, rational functions, and conic sections.
  2. Solve applied problems using the appropriate function.
  3. Be able to use function notation to evaluate expressions and perform operations on functions such as addition, subtraction, multiplication, division, and composition of functions. Be able to find the domain of functions.
  4. Find the inverse of one-to-one functions.
  5. Solve systems of equations, both linear and non-linear.
  6. Work introductory exercises using polar coordinates, parametric functions, and vectors.
  7. Work introductory exercises from topics in discrete mathematics, such as sequences and series.
  8. Solve equations containing trigonometric functions both in routine exercises and applied problems.

Student Learning Outcomes:
Upon successful completion of the course, students should be able to:


1.      Identify and  manipulate polynomial, power, rational, exponential, logarithmic, and trigonometric functions.

2.      Represent a given polynomial, power, rational, exponential, logarithmic,and trigonometric function numerically, symbolically, graphically, and verbally.  Select the appropriate function in applied problems.

3.      Understand and perform addition, subtraction, multiplication, division, and composition of functions.  Perform these operations algebraically, numerically, graphically, and in applied settings.

4.      Understand the abstract concepts of function inverses and one-to-one functions.  Find inverse functions using algebraic, numerical, graphical, and verbal techniques.  Solve problems involving the inverses of (restricted) polynomial, power, rational, exponential, and trigonometric functions.  Use appropriate inverse functions in applications.

5.      Work basic exercises using polar coordinates, parametric functions, vectors, sequences, and series.

6.      Solve equations containing trigonometric functions in routine and applied problems.