MATH& 141 Precalculus I (5 credits)
Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Formerly MATH 121 - CCN
Prerequisite Completion of GSP; or MATH 098 or equivalent with a grade of 2.0 or better; or instructor permission
Course Description
This is the first of two courses in the precalculus sequence, which is designed to prepare students for calculus. Topics include toolkit families of functions – linear, quadratic, polynomial, rational, exponential, logarithmic, absolute value, and square root – with an emphasis on transitioning between verbal, numeric, algebraic, and graphical representations to solve problems. Appropriate use of technology is integrated throughout the course.
Course Content
A. Properties of Functions
Toolkit families of functions - linear, quadratic and polynomial, absolute value, square root, cube root, rational, exponential and logarithmic functions
Four forms of functions – linking verbal, algebraic, numerical and graphical ideas
Domain and range
Composite and combined functions
Even and odd functions
Average rate of change
Inverse functions and their properties
B. Algebraic Techniques
Solving equations involving toolkit families of functions
Solving inequalities involving toolkit families of functions
Properties of exponents and logarithms in context of exponential and logarithmic functions
Distance between two points
C. Graphs of Functions
Graphs of the toolkit functions (linear, quadratic and polynomial, absolute value, square root, cube root, rational, exponential and logarithmic functions)
Transformations (shifts, compressions/stretches, and reflections) of functions
Determining graphical properties of polynomial and rational functions algebraically (degree, maximum number of zeros, maximum number of turns, multiplicity of zeros, vertical asymptotes, horizontal asymptotes, and long-run behavior)
Domain and range – graphical methods
Graphically representing equations and inequalities
D. Applications of Functions
Developing appropriate models for linear and non-linear using technology
Solving application problems such as optimization or growth and decay
Approximate and exact solutions
Reasonableness of solutions
Communication of solution processes
Student Outcomes
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Transition between the four representations of functions (algebraic, numerical, graphical, and verbal) for all toolkit families of functions (linear, quadratic, polynomial, rational, exponential, logarithmic, absolute value and square root functions).
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Analyze the effect of transformations on the behavior of toolkit functions and their properties (including the domain and range), using all four representations of functions.
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Use context to develop viable problem-solving strategies, including the choice of appropriate representations of functions.
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Solve application problems such as average rate of change, initial conditions, optimization, growth and decay using the appropriate toolkit functions or related regression models.
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Evaluate the reasonableness of a problem solution in the context of its mathematical and/or real-world assumptions.
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Communicate solution processes including strategy choices in the context of applied problems.
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Use appropriate technology to model problems, develop strategies, and interpret solutions in context.
Degree Outcomes
Quantitative & Symbolic Reasoning: Graduates utilize mathematical, symbolic, logical, graphical, geometric, or statistical analysis for the interpretation and solution of problems in the natural world and human society.
Critical, Creative and Reflective Thinking: Graduates will evaluate, analyze, synthesize, and generate ideas; construct informed, meaningful, and justifiable conclusions; and process feelings, beliefs, biases, strengths, and weaknesses as they relate to their thinking, decisions, and creations.
Effective Communication: Graduates will be able to craft and exchange ideas and information in a variety of situations, in response to audience, context, purpose, and motivation.
Lecture Contact Hours 50
Lab Contact Hours 0
Clinical Contact Hours 0
Total Contact Hours 50
Potential Methods
Discussions
Written Assignments
Projects
Case Studies
Presentations
Homework
Quizzes
Objective Tests
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