MATH& 141 Precalculus I (5 credits)
Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Formerly MATH 121 - CCN
Prerequisite MATH 098 with at least a 2.0 grade or placement test score above MATH 098 or co-enrolled in MATHL 141.
Course Description
Families of functions, their properties, graphs and applications. Functions include: polynomial, rational, exponential, logarithmic functions and combinations of these. Solve related equations and inequalities. Data analysis, introductory mathematical modeling. Develop competency with a graphing calculator.
Student Outcomes
A(1), C. Four Forms of Functions
1. Solve equations algebraically and graphically involving linear, quadratic, polynomial, rational, exponential, logarithmic, absolute value and square root functions.
2. Solve linear, polynomial, and rational inequalities algebraically and graphically.
3. Link verbal, algebraic, numerical, and graphical solutions with each other.
4. Describe or determine the average rate of change of a function verbally, algebraically, numerically, and graphically.
5. Describe and determine inverse functions verbally, algebraically, numerically, and graphically.
6. Perform transformations (shifts, compressions/stretches, and reflections) of functions given in algebraic, numerical, and graphical form for functions such as linear, quadratic, exponential, logarithmic, absolute value, and square root.
A(2), C. Properties of Functions
7. Determine domain and range of functions.
8. Use the properties of logarithms to simplify or evaluate logarithmic expressions.
9. Determine from a graph or equation if a function is even, odd, or neither.
10. Determine the properties of polynomial and rational functions such as degree, maximum number of zeros, maximum number of turns, multiplicity of zeros, vertical asymptotes, horizontal asymptotes, and long-run behavior.
A(3). The Algebra of Functions
11. Simplify, evaluate, and find the domains of combined functions and composite functions.
12. Determine the equations of polynomial, exponential, and logarithmic functions algebraically
A(4). Graphs of Functions
13. Identify and sketch graphs of the elementary functions (constant, linear, quadratic, third degree and higher polynomial, absolute value, square root, cube root, rational, exponential (base 10 and base e), logarithmic (base 10 and base e)).
14. Graph elementary functions without a calculator by using methods such as a table of values, slope-intercept, characteristic shape of the function, degree, maximum number of zeros, maximum number of turns, multiplicity of zeros, vertical asymptotes, horizontal asymptotes, and long-run behavior.
A(5). Applications of Functions
15. Solve application problems such as optimization or growth and decay using the appropriate elementary functions.
16. Interpret the solution in the context of the problem and evaluate the reasonableness of the solution.
B. Analytic Geometry
17. Calculate the distance and midpoint between two points.
18. Use the equation of a circle to produce a graph and find the equation of a circle from a graph.
D. Data analysis and Mathematical modeling
19. Interpret and analyze linear and non-linear data in numeric, graphic, and algebraic form to develop an appropriate model using technology.
E. Graphing Calculator
20. Graph functions on a calculator and analyze them using an appropriate window.
21. Find minima, maxima, zeros, long-range behavior, and asymptotes using a graphing calculator.
F. General Content
22. Write clear, correct, and complete solutions to mathematical problems utilizing proper mathematical notation and appropriate language.
23. Communicate the difference between an exact and an approximate solution and determine which is more appropriate for a given problem.
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