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|MAT140 - Precalculus|
Catalog Description: Studies polynomial, rational, exponential, logarithmic, and trigonometric functions and their inverses. Four class hours. Not open for credit to students who have credit in MAT 141 or higher. Prerequisite: MAT 136 (with a minimum grade of C) or equivalent by placement.
Lecture: 4 hrs.
Course Student Learning Outcomes (CSLOs):
Upon successful completion of the course, students will be able to perform the following:
1. Given functions of the form y = f(x), evaluate this function at a point, sketch the graph, apply geometric transformations, compute the domain and/or compute combinations and compositions of these functions.
2. Given a function, compute the inverse of this function.
3. Compute the zeros of a polynomial function.
4. Given two complex numbers, add, subtract, multiply, and divide these numbers and express the result in standard complex form.*
5. Apply the basic properties of logarithms to expand or condense an expression into an equivalent form.
6. Solve exponential and logarithmic equations and application problems.
7. Solve application problems involving right triangle trigonometry.*
8. Compute trigonometric values of any angle expressed in radians or degrees, and the inverse trigonometry values of any number in the domain of that function.
9. Construct and analyze graphs of the form y = Asin(Bx + C) + D or Acos(Bx + C) + D and construct and analyze the graph of y = tan(x).
10. Use basic trigonometric identities to rewrite trigonometric expressions and verify other identities.
11. Find solutions to trigonometric equations over a stated interval by collecting terms, factoring, or extracting square roots.
12. Apply the law of sines and cosines to solve problems involving acute and obtuse triangles.
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
I. REVIEW - EQUATIONS AND INEQUALITIES
A. Absolute Value in Equations and Inequalities
B. Polynomial & Rational Inequalities
II. GRAPHS AND FUNCTIONS
A. Rectangular Coordinate Systems; Graphing
B. Relations and Functions
C. Functions: Graphs and Properties
D. Linear Relations and Functions
E. Graphing Polynomial Functions
F. Graphing Rational Functions
G. Composite and Inverse Functions
III. POLYNOMIAL FUNCTIONS AND THEORY OF EQUATIONS
A. Synthetic Division
B. Remainder and Factor Theorems
C. Fundamental Theorem of Algebra
D. Isolating Real Zeros
E. Finding Rational Zeros
IV. EXPONENTIAL AND LOGARITHMIC
A. Exponential Functions
B. Logarithmic Functions
C. Properties of Logarithmic Functions
D. Logarithms to Various Bases
E. Exponential and Logarithmic Equations
V. TRIGONOMETRIC FUNCTIONS
A. The Wrapping Function
B. Circular Functions
D. Trigonometric Functions
E. Graphs of Trigonometric Functions
F. Graphing y = A sin (Bx + C) and y = A cos (Bx + C)
G. Inverse Trigonometric Functions
VI. TRIGONOMETRIC IDENTITIES AND CONDITIONAL EQUATIONS
A. Basic Identities and Their Uses
B. Sum, Difference, and Cofunction Identities
C. Double-Angle and Half-Angle Identities
D. Product and Factor Identities
VII. ADDITIONAL TOPICS IN TRIGONOMETRY
A. Solutions of Right Triangle
B. Law of Sines
C. Law of Cosines
D. Vectors (optional)
Effective Term: Fall 2012