- University of California, Irvine
- 8 weeks
- Paid Certificate Available
This course covers mathematical topics in college algebra, with an emphasis on functions. The course is designed to help prepare students to enroll for a first semester course in single variable calculus.
Upon completing this course, you will be able to:
1. Solve linear and quadratic equations
2. Solve some classes of rational and radical equations
3. Graph polynomial, rational, piece-wise, exponential and logarithmic functions
4. Find integer roots of polynomial equations
5. Solve exponential and logarithm equations
6. Understand the inverse relations between exponential and logarithm equations
7. Compute values of exponential and logarithm expressions using basic properties
Course Overview and Algebra Review
We begin with an overview of the course and an opportunity to review and practice some of the prerequisite algebra skills needed for success in this course.
Linear Equations and Inequalities. Absolute Value Equations and Inequalities.
In this module, we will learn to solve linear and absolute value equations and inequalities. We will also explore a range of story problems which can be solved utilizing linear equations.
In this module, we explore a variety of methods for solving quadratic equations.
Rational and Radical Equations.
We begin this module by practicing manipulations of rational expressions using basic properties. We then utilize these manipulations to solve rational and radical equations.
Functions. Graphs of Functions. Transformations of Functions.
In this module, we define the notion of "function". We learn to distinguish between functions and non-functions in graphical, symbolic and tabular form. Finally, we will explore graphs of functions and how these graphs behave under linear transformations.
Quadratic Functions. Inverse Functions. Polynomials.
In this module, we explore quadratic equations and graphs. We also introduce the notion of inverse functions. Finally, we will learn about polynomial properties and practice some methods for polynomial root finding.
Exponential and Logarithmic Equations.
Exponential and logarithmic functions are two important functions that are useful in applications of calculus. We will discuss properties and graphs of these special functions. We will also learn to solve equations involving exponential and logarithmic functions.
Pre-Calculus Functions Final Exam
Now is your opportunity to review the topics from this course. The comprehensive final exam is your chance to demonstrate your conceptual understandings of functions and algebraic computational skills.
Sarah Eichhorn and Rachel Lehman
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