2024-2025 Yavapai College Catalog
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Jul 12, 2024
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# MAT 182 - Precalculus (Algebra)

Description: Topics from college algebra essential to the study of calculus and analytic geometry. Includes the definition of and operations with functions, identifying characteristics of and graphing functions, and applications of functions.  Types of functions include a review of linear functions and an in-depth examination of nonlinear functions (quadratic, polynomial and power, rational, exponential and logarithmic).  Note: Computer use and/or graphing calculator required.

Prerequisites: MAT 097  or a satisfactory score on the mathematics skills assessment.

Credits: 3
Lecture: 3
Lab: 0

Course Content:
1. Functions (definition, representations, transformations and symmetry, operations, composition, inverse, domain and range, average rate of change, difference quotient).
2. Polynomial and Power Functions (real and complex zeros, relative max/min, end behavior, graphs, equations and inequalities, and applications)
3. Rational Functions (domain, asymptotes, intercepts, graphs, equations and inequalities, applications)
4. Exponential Functions (characteristics, graphs, equations and applications)
5. Logarithmic Functions (characteristics, graphs, properties, equations and applications)
6. Graphing technology

Learning Outcomes:
1. Use definitions and operations associated with functions, including inverses, combinations, and compositions. (1)
2. Represent functions in a variety of ways; numeric, symbolic, graphic, and verbal. (1-5)
3. Interpret functions given in a variety of ways; numeric, symbolic, graphic and verbal. (1-5)
4. Solve equations and inequalities using a variety of techniques including symbolic and graphical. (2-6)
5. Identify specific characteristics of each type of function such as slope, vertex, zeros, relative max/min, end behavior, asymptotes, etc. (1-5)
6. Graph basic functions based on their characteristics (1-5)
7. Use transformations to reflect changes made to basic functions. (1-5)
8. Apply mathematics in context. (1-6)
9. Model real situations using mathematics. (1-6)
10. Utilize graphing technology when appropriate (graphing functions, solving equations). (1-6)