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# Pre-calculus

 As a result of home and classroom study, the students at the termination of this course will demonstrate the following knowledge and skills: OUTCOMES ACTIVITIES ASSESSSMENT Demonstrate knowledge of the basic properties of functions in order to apply this knowledge to analyze and graph different types of functions 1.Determine if a relation is a function 2.Find the domain and range of a function. 3.Find the intercepts of a function algebraically. 4.Add, subtract, multiple, and divide functions and determine the domain of the resulting functions. 5.Use the graph of a function to identify domain and range, intervals of increase and decrease, relative extrema, and intercepts. 1. Hand-in assignments. 2. In-class problems. 3. In-class tests. Use the built-in graphing capabilities of a graphing calculator in order to graph and analyze functions 1.Graph functions. 2.Adjust the graphing window to obtain a complete graph. 3.Use ZOOM and TRACE appropriately. 4.Use TABLE and TBLSET appropriately. 5.Use other features such as ‘zero’, ‘minimum’, ‘maximum’, and ‘intersect’ appropriately. 1. Hand-in assignments. 2. In-class problems. 3. In-class tests. Review and deepen understanding of linear functions 1.Identify linear functions from a table of values 2.Find the equation of a linear function given certain information. 3.Model real-world applications using linear functions. 4.Fit a linear function to a table of data. 1. Hand-in assignments. 2. In-class problems. 3. In-class tests. Perform operations on functions 1.Use vertical and horizontal shifts, vertical and horizontal reflections, and vertical stretching and shrinking to graph functions 2.Graph piecewise functions. 3.Evaluate the sum, difference, product, quotient, and composition of functions 4.Evaluate and graph the inverse of a function. 1. Hand-in assignments. 2. In-class problems. 3. In-class tests. Recognize and analyze polynomial functions. 1.Categorize functions as linear, quadratic, exponential, or polynomial from their graphs. 2.Find the domain range and graph of rational functions. 1. Hand-in assignments. 2. In-class problems. 3. In-class tests. Use logarithmic and exponential functions to model real-world situations 1.Calculate logarithms with base 10, base e, and an arbitrary base. 2.Graph logarithmic functions and their inverses, the exponential functions. 3.Use the graphing calculator to solve application problems, including growth and decay. 1. Hand-in assignments. 2. In-class problems. 3. In-class tests. Demonstrate an understanding of the six trigonometric functions 1.Calculate the six trigonometric functions of an acute angle in a right triangle. 2.Identify the period and amplitude of general trigonometric functions. 3.Graph trigonometric functions. 4.Derive basic trigonometric identities from the Pythagorean Theorem. 5.Use the Law of Sines and the Law of Cosines to solve for the missing parts of a triangle. 6.Solve related application problems. 1. Hand-in assignments. 2. In-class problems. 3. In-class tests.