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Course: College Algebra

Differential Calculus Overview

Course Description: 

The concepts studied in college algebra form a bedrock for a deeper understanding of mathematics. Throughout this course, students will develop their critical thinking skills as they analyze and devise solutions to problems relevant to this level of mathematics. In this course, students will become familiar with the properties of various basic functions, such as polynomials, rational expressions, radicals, logarithmic, and exponentials. Students will study various strategies for identifying the roots of different functions in detail. Students will discuss graphing techniques. Students will be able to identify exponential and logarithmic functions and become familiar with their applications.

Prerequisite: Foundations of Algebra

Course Topics

  • Function Notations
  • Domains, Co-Domain, Range
  • Function Types
    • Onto [Surjective]
    • One-To-One [Injective]
    • One-To-One Correspondence [Bijective]
    • Compositions
  • Inverse Functions

Properties of Exponents

  • Symbolical Solutions
  • Proportionality
    • Directly Proportional
    • Indirectly Proportiona
  • Distribution Property
  • Grouping Terms
  • Binomials and Trinomials
  • Special Forms
  • Completing the Square
  • The Quadratic Formula
  • Quadratic Forms
  • Inequalities
  • Graphing
  • Applications: Max and Min
  • Fundamental Theorem of Algebra
  • Rational Roots Theorem
  • Inequalities
  • The Basics of Complex Numbers
  • Radical, Rational, Polynomials
  • Zero-Factor Property
  • Graphing Equations
  • Exponential Equations
  • Logarithmic Equations

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