MTH196 - Advanced Functions

Outline info
Last revision date 2017-05-29 00:38:47.205
Last review date 2017-07-17 00:16:15.283

Subject Title
Advanced Functions

Subject Description
This course is designed to develop students' skills with functions, broadening the understanding of their properties and applications.

Credit Status

Learning Outcomes
Upon successful completion of this subject the student will be able to:

1. Investigate the properties of polynomial, rational, logarithmic, and trigonometric functions

2 .Develop techniques for combining functions

3 .Demonstrate an understanding of rates of change, the graphical definition of a derivative, and the relationship between the derivative of a function and its graph.

4. Apply the skills gained in solving problems with functions

Essential Employability Skills
Respond to written, spoken, or visual messages in a manner that ensures effective communication.

Execute mathematical operations accurately.

Apply a systematic approach to solve problems.

Use a variety of thinking skills to anticipate and solve problems.

Locate, select, organize, and document information using appropriate technology and information systems.

Analyze, evaluate, and apply relevant information from a variety of sources.

Show respect for diverse opinions, values, belief systems, and contributions of others.

Interact with others in groups or teams in ways that contribute to effective working relationships and the achievement of goals.

Manage the use of time and other resources to complete projects.

Take responsibility for one's own actions, decisions, and consequences.

Cheating and Plagiarism
Each student should be aware of the College's policy regarding Cheating and Plagiarism. Seneca's Academic Policy will be strictly enforced.

To support academic honesty at Seneca College, all work submitted by students may be reviewed for authenticity and originality, utilizing software tools and third party services. Please visit the Academic Honesty site on for further information regarding cheating and plagiarism policies and procedures.

All students and employees have the right to study and work in an environment that is free from discrimination and/or harassment. Language or activities that defeat this objective violate the College Policy on Discrimination/Harassment and shall not be tolerated. Information and assistance are available from the Student Conduct Office at

Accommodation for Students with Disabilities
The College will provide reasonable accommodation to students with disabilities in order to promote academic success. If you require accommodation, contact the Counselling and Disabilities Services Office at ext. 22900 to initiate the process for documenting, assessing and implementing your individual accommodation needs.

MTH079/MTH149 (grade B or higher) or Grade 11U/12C math 

Topic Outline
1. Polynomial Functions
1.1 Power Functions
1.2 Characteristics of Polynomial Functions
1.3 Equations and Graphs of Polynomial Functions
1.4 Transformations
1.5 Slopes of Secants and Average Rate of Change
1.6 Slopes of Tangents and Instantaneous Rate of Change

2. Polynomial Equations and Inequalities
2.1 The Remainder Theorem
2.2 The Factor Theorem
2.3 Polynomial Equations
2.4 Families of Polynomial Functions
2.5 Solve Inequalities Using Technology
2.6 Solve Factorable Polynomial Inequalities Algebraically

3. Rational Functions
3.1 Reciprocal of a Linear Function
3.2 Reciprocal of a Quadratic Function
3.3 Rational Functions of the Form  f (x) = ax + b / cx + d
3.4 Solve Rational Equations and Inequalities
3.5 Making Connections With Rational Functions and Equations

4. Trigonometry
4.1 Radian Measure
4.2 Trigonometric Ratios and Special Angles
4.3 Equivalent Trigonometric Expressions
4.4 Compound Angle Formulas
4.5 Prove Trigonometric Identities

5. Trigonometric Functions
5.1 Graphs of Sine, Cosine, and Tangent Functions
5.2 Graphs of Reciprocal Trigonometric Functions
5.3 Sinusoidal Functions of the Form and f (x) = a sin [ k (x-d) ] + c and f (x) = a cos [ k (x-d )] + c
5.4 Solve Trigonometric Equations
5.5 Making Connections and Instantaneous Rate of Change

6. Exponential and Logarithmic Functions
6.1 The Exponential Function and Its Inverse
6.2 Logarithms
6.3 Transformations of Logarithmic Functions
6.4 Power Law of Logarithms
6.5 Making Connections: Logarithmic Scales in the Physical Sciences

7. Tools and Strategies for Solving Exponential and Logarithmic Equations
7.1 Equivalent Forms of Exponential Equations
7.2 Techniques for Solving Exponential Equations
7.3 Product and Quotient Laws of Logarithms
7.4 Techniques for Solving Logarithmic Equations
7.5 Making Connections: Mathematical Modeling With Exponential and Logarithmic Equations

8. Combining Functions
8.1 Sums and Differences of Functions
8.2 Products and Quotients of Functions
8.3 Composite Functions
8.4 Inequalities of Combined Functions
8.5 Making Connections: Modelling With Combined Functions

Mode of Instruction
Your professor will use a variety of appropriate teaching modes and techniques, such as the following:  lecture, question and answer, tutorials, classroom discussion, group work,
individual and/or group presentation, computer-aided instruction, consultation, etc. 

Prescribed Texts
Erdman, W. et al.  Advanced Functions 12.  MHR.

Reference Material

Required Supplies

Promotion Policy

Grading Policy
A+ 90%  to  100%
A 80%  to  89%
B+ 75%  to  79%
B 70%  to  74%
C+ 65%  to  69%
C 60%  to  64%
D+ 55%  to  59%
D 50%  to  54%
F 0%    to  49% (Not a Pass)
EXC Excellent
SAT Satisfactory
UNSAT Unsatisfactory

For further information, see a copy of the Academic Policy, available online ( or at Seneca's Registrar's Offices.

Modes of Evaluation
To be successful in this course, you must complete all course work as specified and achieve an overall grade of 50% or higher. For further information on evaluation and academic standing, see a copy of the Academic Policy available at Seneca registration offices.

Term Work: All term work assignments must be completed prior to the time of the examination. Unless students have been granted an extension in advance, late take-home
assignments will be penalized one letter grade per day and will not be graded after one week (there is no provision for rewriting late assignments, regardless of the grade).
Students must contact faculty in advance of due date to discuss extensions.

If a student has to miss any in-class quiz/test, he/she must notify the faculty via email or phone messages prior to start time of the quiz/test date.  Valid documentation
(such as original stamped doctor's note) must be submitted to the faculty on or before the next scheduled class.  Make-up opportunities may be arranged at the Test Centre.

Grading Scheme:  
Test 1 15%
Test 2 10%
Test 3 15%
Test 4 10%
Assignments (3) 15%

Approved by: Fiona Bain-greenwood