LSC-CyFair Math Department

**Catalog Description:**In-depth study and Applications of Polynomial, rational, radical, absolute-Value, piecewise Defined, Exponential and logarithmic functions, equations, inequalities, graphing skills and systems of equations using matrices. Additional topics such as sequences, series, probability, conics and Inverses may be included.

**Course Learning Outcomes:**

• Demonstrate and apply knowledge of properties of functions, including domain and range, operations, compositions, inverses and piecewise defined functions.

• Recognize, graph and apply polynomial, rational, radical, exponential, logarithmic and absolute value functions and solve related equations.

• Apply graphing techniques.

• Evaluate all roots of higher degree polynomial and rational functions.

• Recognize, solve and apply systems of linear equations using matrices.

• Solve absolute value, polynomial and rational inequalities.

Lecture Hours: 3

Lab Hours: 0

External Hours: 0

Total Contact Hours: 48

**Prerequisites:**

**Corequisites:**

**Required Materials**Lial, Hornsby, Schneider, Daniels;

Calculator:

Graphing Calculator required. TI 83, TI 84 or TI 86 series calculators recommended.

Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models.

Neither cell phones nor PDA’s can be used as calculators. Calculators may be cleared before tests.

**Textbook Sections**In some sections, not all objectives are covered. Required objectives are listed below. To clarify, examples that accompany objectives that can be skipped are listed. Instructors may cover additional objectives at their discretion. Although instructors may not necessarily assign all of the problems in the Suggested Exercise Blocks, in order to demonstrate proficiency in the learning outcomes of this course, students should be able to do any of the problems in these lists.

Suggestions for Writing College Algebra Exams

Especially for new faculty, these suggestions my prove helpful in helping to plan and prepare exams in College Algebra.

Section | Objectives to Cover | Examples to Skip | Suggested Exercises |

1.3 Complex Numbers | - Basic Concepts of Complex Numbers - Operations on Complex Numbers |
None | 7 - 80, 85 - 96 |

1.4 Quadratic Equations | - Solving a Quadratic Equation - Completing the Square - The Quadratic Formula - Solving for a Specified Variable |
7,9 | 13 - 48, 51 - 65, 71 - 78 |

1.5 Applications and Modeling with Quadratic Equations | - Geometry Problems - Using the Pythagorean Theorem - Height of a Projected Object |
4 | 1 - 44 |

1.6 Other Types of Equations and Applications | - Rational Equations - Equations with Radicals - Equations with Rational Exponents - Equations Quadratic in Form |
3 | 7 - 26, 35 - 88 |

1.7 Inequalities | - Linear Inequalities - Three-part Inequalities - Quadratic Inequalities - Rational Inequalities |
None | 13 - 24, 29 - 52, 55 - 92 |

1.8 Absolute Value Equations and Inequalities |
- Basic Concepts |
4, 5, 6 | 9 - 66 |

2.1 Rectangular Coordinates and Graphs | - The Distance Formula - The Midpoint Formula - Graphing Equations in Two Variables |
1, 3, 4, 6, 7 | 11 - 18, 31 - 36, 43 - 54 |

2.2 Circles | - Center-Radius Form - General Form |
6 | 1 - 16, 19 - 30 |

2.3 Functions | - Relations and Functions - Domain and Range - Determining Functions from Graphs or Equations - Function Notation - Increasing, Decreasing and Constant Functions |
None | 1 - 86 |

2.5 Equations of Lines and Linear Models | - Point Slope Formula - Slope Intercept Form - Vertical and Horizontal Lines - Parallel and Perpendicular Lines |
7, 8 | 5 - 26, 28 - 37, 39 - 54 |

2.6 Graphs of Basic Functions | - Continuity - The Identity, Squaring and Cubing Functions - The Square Root and Cube Root Functions - The Absolute Value Function - Piecewise Defined Functions (Skip Greatest Integer Function) - The relation x = y^{2} |
3, 4 | 1 - 5, 7 - 42 |

2.7 Graphing Techniques | - Stretching and Shrinking - Reflecting - Symmetry - Even and Odd Functions - Translations |
None | 1 - 84, 93, 94 |

2.8 Function Operations and Composition | - Arithmetic Operations on Functions - Composition of Functions and Domain |
4 | 1 - 14, 23 -30, 47 - 54, 63 - 78, 83 - 86 |

3.1 Quadratic Functions and Models | - Quadratic Functions - Graphing Techniques - Completing the Square - The Vertex Formula |
6 | 1 - 40, 53, 54 |

3.2 Synthetic Division | - Synthetic Division (skip Division Algorithms) - Evaluating Polynomial Functions Using the Remainder Theorem - Testing Potential Zeros |
None | 1 - 18, 27 - 58 |

3.3 Zeros of Polynomial Functions | - Factor Theorem - Rational Zeros Theorem |
4, 5, 6, 7 | 5 - 22, 27 - 30, 35 - 48 |

3.4 Polynomial Functions: Graphs, Applications and Models | - Graphs of f(x) = ax^{n}- Graphs of General Polynomial Functions - Behavior at Zeros - Turning Points and End Behavior - Graphing Techniques |
5, 6, 7, 8 | 1 - 46, 71 - 88 (questions 75 - 82, use the zero feature in the TI 83/84) |

3.5 Rational Functions: Graphs, Applications and Models | - The Reciprocal Functions f(x) = 1/x- The Function f(x) = 1/x^{2} |
5, 6, 7, 8, 9, 10 | 1 - 28, 37 - 46 (identify vertical asymptotes only), 61 - 100 (identify zeroes and vertical asymptotes only) |

4.1 Inverse Functions | - One-to-one Functions - Inverse Functions - Equations of Inverses |
9 | 1 - 20, 41 - 82 |

4.2 Exponential Functions | - Exponents and Properties - Exponential Functions - Exponential Equations - Compound Interest - The Number e and Continuous Compounding |
11 | 1 - 96 |

4.3 Logarithmic Functions | - Logarithms - Logarithmic Equations - Logarithmic Functions - Properties of Logarithms |
7 | 3 - 36, 39 - 84 |

4.4 Evaluating Logarithms and the Change of Base Theorem | - Common Logarithms - Natural Logarithms - Logarithms with Other Bases |
2, 3, 4, 5, 6, 7, 9 | 11 - 26, 79 - 90 |

4.5 Exponential and Logarithmic Equations | - Exponential Equations - Logarithmic Equations |
10, 11 | 1 - 78 |

4.6 Applications and Models of Exponential Growth and Decay | Select a Few of the Applications to Cover | 3, 5, 6 | Selected Problems from 5 - 16, 25 - 30, 35 - 38, 45 - 50 |

5.1 Systems of Linear Equations | - Linear Systems - Substitution Method - Elimination Method - Special Systems |
5, 6, 7, 8, 9 | 7 - 39 |

5.2 Matrix Solutions of Linear Systems |
- The Gauss-Jordan Method (Use the rref feature on a graphing calculator to row reduce matrices) |
1 - 42 (use the rref feature on a calculator to row reduce matrices) |

Getting Started Assignments:**Review exercises in MyMathLab that can be copied into your own course. Copy 6 "getting Started" assignments from the review chapter from jezek91587**

Suggested Review for Final Exam

This General Review can be used as a review / practice test for the Final Exam in College Algebra. Use of this review is optional.