| Originator: | Clifford, Laurel Status: Approved Department: MAT Mathematics |
| Date Created: | 09/09/2016 Submitted: 09/29/2016 Completed: 12/27/2016 |
| Effective Semester: | Fall |
| Catalog Year: | 2017-18 |
| Course Prefix: | MAT |
| Course Number: | 151 |
| Course Full Title: | College Algebra |
| Old course information: | |
| Reason for Evaluation: | Prerequisite Change Description Change Goals, Competencies and/or Objectives Change |
| Current Credit: | 4 |
| Lecture Hours: | 4 |
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| If the credit hour change box has been marked, please provide the new credit hour: | |
| New Lecture Hours: | |
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| SUN Course?: | Yes |
| AGEC Course?: | Yes |
| Articulated?: | Yes |
| Transfer: | ASU NAU UA |
| Prerequisite(s): | Grade of C or better in MAT 121 or appropriate score on placement test |
| Corequisite(s): | none |
| Catalog Course Description: | College Algebra is the study and analysis of linear, polynomial, exponential, and logarithmic functions, equations and inequalities, conic sections, systems of equations and matrices, and sequences and series, with an emphasis on problem solving and multiple representations. |
| Course Learning Outcomes: | 1. Represent relationships between variable quantities using linear, quadratic, polynomial, rational, exponential, and logarithmic functions, sequences, series, and conic sections (2, 3, 5, 6) 2. Examine function behavior and characteristics both within a specific function class and between different function classes (2, 3, 5, 6) 3. Create accurate and appropriate mathematical models to solve problems from information given in context (2, 3, 5, 6) 4. Solve a variety of equations and inequalities using graphic, numeric, analytic, and matrix methods (2, 3, 5, 6) |
| Course Competencies: | Competency 1: Express relationships between two variables as functions with unique, identifiable properties
Objective 1.1: Determine if mathematical relationships given in various representations (graph, table, mapping, verbal, etc.) represent functions Objective 1.2: Determine if mathematical relationships given in various representations represent one to one functions Objective 1.3: Explain the contextual interpretation of input and output values given in function notation Objective 1.4: Calculate output values for functions given in various representations Objective 1.5: Identify the domain for functions given in various representations Objective 1.6: Identify the range for functions given in various representations Objective 1.7: Differentiate among the shapes of basic 'parent' functions, including (identity, squaring, cubing, square root, cube root, absolute value) Objective 1.8: Contrast the unique properties of basic function 'families' (linear, quadratic, cubing, square root, cube root, absolute value) Objective 1.9: Determine the geometric transformations (translations, reflections, stretches/compressions) of functions given in various representations Objective 1.10: Create graphs for functions using the basic parent function shape and geometric transformations Objective 1.11: Create equations for functions using the basic parent function shape and geometric transformations Objective 1.12: Evaluate piecewise-defined functions for given domain values Objective 1.13: Graph piecewise-defined functions accurately including open and closed endpoints as appropriate to the function conditions Objective 1.14: Create piecewise-defined functions from graphs and verbal descriptions Objective 1.15: Identify the type of symmetry a function exhibits (if any) Objective 1.16: Evaluate the difference quotient for a variety of functions Objective 1.17: Explain the relationship between the difference quotient and rate of change (slope) Objective 1.18: Analyze the behavior of functions given in various representations including extrema, and increasing, decreasing, and/or constant intervals Objective 1.19: Assess functions given in various representations for intervals of continuity Objective 1.20: Combine two or more functions given in various representations using function operations (addition, subtraction, multiplication, division) Objective 1.21: Determine the result of the composition of functions given in various representations Objective 1.22: Create the inverse of a function in various formats Objective 1.23: Identify restrictions on the domain of inverse functions Competency 2: Create linear function models to solve contextual problems Objective 2.1: Calculate the average rate of change between ordered pairs of data presented in graphic, numeric, analytic and verbal representations Objective 2.2: Explain the meaning of the average rate of change in context Objective 2.3: Identify key features of linear functions, including domain, range, slope, intercepts, and increasing/decreasing behavior Objective 2.4: Create multiple representations (table, graph, equation) of linear functions from contextual data Objective 2.5: Distinguish linear behavior from nonlinear behavior Objective 2.6: Explain the contextual implications of linear function behavior Objective 2.7: Evaluate linear functions expressed in multiple representations for given input values Objective 2.8: Solve linear equations using graphic, numeric, and analytic methods Objective 2.9: Generate solutions to linear inequalities from related linear equations Competency 3: Create polynomial function models to solve contextual problems Objective 3.1: Identify key features of polynomial functions, including domain, range, extrema, continuity, increasing/decreasing behavior intervals, intercepts, symmetry, and end behavior Objective 3.2: Create multiple representations (table, graph, equation) of polynomial functions from contextual data Objective 3.3: Relate the number of complex zeros to the degree of the polynomial function Objective 3.4: Determine the complex zeros for polynomial functions using numeric, graphic, and analytic methods Objective 3.5: Evaluate polynomial functions expressed in multiple representations for given input values Objective 3.6: Generate solutions to polynomial inequalities from related polynomial equations Objective 3.7: Explain the contextual implications of polynomial function behavior Objective 3.8: Solve quadratic equations for real and nonreal solutions using graphic, numeric, and analytic methods Objective 3.9: Generate solutions to quadratic inequalities from related quadratic equations Objective 3.10: Determine the existence of nonreal solutions to quadratic equations Objective 3.11: Identify the vertex of quadratic functions given in various representations Objective 3.12: Translate among various representations of quadratic functions via completing the square, factoring, and simplification Objective 3.13: Identify the transformations of quadratic functions from the basic squaring function Objective 3.14: Explain the effect of geometric transformations on quadratic function characteristics Objective 3.15: Explain the contextual implications of the vertices and behavior of quadratic functions in context Competency 4: Create rational function models to solve contextual problems Objective 4.1: Identify domain restrictions for rational functions Objective 4.2: Distinguish among possible discontinuities of rational functions Objective 4.3: Identify key features of rational functions, including domain, range, asymptotes, continuity, increasing/decreasing behavior intervals, intercepts, symmetry, and end behavior Objective 4.4: Explain the contextual implications of rational functions' asymptotic behavior Objective 4.5: Evaluate rational functions expressed in multiple representations for given input values Objective 4.6: Solve rational equations using graphic, numeric, and analytic methods Objective 4.7: Generate solutions to rational inequalities from related rational equations Objective 4.8: Identify extraneous solutions of rational equations and inequalities Objective 4.9: Create multiple representations (table, graph, equation) of rational functions from contextual data and transformations Objective 4.10: Translate between representations of rational functions Objective 4.11: Explain the effect of geometric transformations on rational function characteristics Competency 5: Create transcendental function models (exponential, logarithmic) to solve contextual problems Objective 5.1: Identify features of exponential functions, including domain, range, asymptotes, continuity, increasing/decreasing behavior intervals, intercepts and end-behavior Objective 5.2: Create multiple representations (table, graph, equation) of exponential functions from contextual data and transformations Objective 5.3: Evaluate exponential functions expressed in multiple representations for given input values Objective 5.4: Identify the transformations of exponential functions from their basic 'parent' function Objective 5.5: Explain the effect of geometric transformations on exponential function characteristics Objective 5.6: Evaluate exponential functions for given input values in context Objective 5.7: Contrast the properties of exponential functions with linear and polynomial functions Objective 5.8: Relate the logarithmic function to the exponential function via inverse function concepts Objective 5.9: Convert equations between exponential and logarithmic form Objective 5.10: Explain the contextual implications of the behavior of transcendental functions Objective 5.11: Identify features of logarithmic functions, including domain, range, asymptotes, continuity, increasing/decreasing behavior intervals, intercepts, and end behavior Objective 5.12: Create multiple representations (table, graph, equation) of logarithmic functions from contextual data Objective 5.13: Evaluate logarithmic functions expressed in multiple representations for given input values Objective 5.14: Identify the transformations of logarithmic functions from their basic 'parent' function Objective 5.15: Explain the effect of geometric transformations on logarithmic function characteristics Objective 5.16: Rewrite logarithmic expressions into equivalent forms via the product, quotient, and power properties of logarithms Objective 5.17: Solve exponential equations using graphic, numeric and symbolic methods Objective 5.18: Generate solutions to exponential inequalities using related exponential equations Objective 5.19: Solve logarithmic equations using graphic, numeric and symbolic methods Objective 5.20: Generate solutions to logarithmic inequalities using related exponential equations Objective 5.21: Solve applied problems using transcendental equations Objective 5.22: Model growth and decay using transcendental functions Competency 6: Create equations of conic sections to solve problems Objective 6.1: Identify the conic section type (circle, parabola, hyperbola, ellipse or degenerate) from its equation Objective 6.2: Rewrite conic section equations from general form to transformation-related form via completing the square Objective 6.3: Identify the major features of conic sections, such as center, radius, major and minor axes and their endpoints, intercepts, asymptotes as appropriate to the conic section type Objective 6.4: Create equations for conic sections from key features given in context Competency 7: Create mathematical models for systems of equations to solve contextual problems Objective 7.1: Calculate solutions to systems of equations of two variables using analytic methods (substitution, elimination) Objective 7.2: Calculate solutions to systems of equations of two variables using graphic methods Objective 7.3: Calculate solutions to systems of multivariable linear equations using matrix row operations (reduced row-echelon form) Objective 7.4: Calculate solutions to systems of multivariable linear equations using matrix equations and inverse matrices Objective 7.5: Select the most efficient solution method for a given system of equations Objective 7.6: Create systems of equations for relationships expressed contextually Objective 7.7: Determine when a unique solution to a system of equations does not exist Objective 7.8: Determine when a system of equations has multiple solutions Objective 7.9: Create matrix representations of contextual data Objective 7.10: Calculate matrix operations (addition, subtraction, scalar multiplication, multiplication) Competency 8: Create mathematical models for sequences and series to solve contextual problems Objective 8.1: Identify patterns in numerical sequences Objective 8.2: Distinguish between recursive and general definitions of sequences Objective 8.3: Select appropriate sequence and series models for data given in context Objective 8.4: Generate sequence values from recursive and general formulas Objective 8.5: Create general formulas for arithmetic and geometric sequences Objective 8.6: Generate values for series from partial sum and summation notation Objective 8.7: Create general formulas expressed in summation notation for series Objective 8.8: Differentiate between converging and diverging infinite sequences Objective 8.9: Differentiate between converging and diverging infinite series Objective 8.10: Calculate the limit of a converging infinite geometric series Objective 8.11: Identify patterns within the coefficients and powers in binomial expansion of (a + b)^n Objective 8.12: Calculate expansion of binomials (u + v)^n involving positive and negative coefficients and exponents |