Welcome to Math 1431 Notes’s

Contents:

• Welcome

Chapter 1:

• Section 1.6
  • Review
  • Application Problem(s)
  • Solving Equations
• Section 1.7
  • Review of concepts
  • Linear Inequality
  • Nonlinear Inequality
    • Rational Inequality
• Section 1.8
  • Review
  • Absolute Value Equations
  • Absolute Value Inequality
    • \(|X|<k\)
    • \(|X|>k\)

Chapter 2:

• Section 2.1
  • Change, Distance, Midpoint
• Section 2.2
  • Completing the Square
  • General to Standard Form Circle Equation
• Section 2.3
  • Evaluate vs. Solve
  • Basic Function Arithmetic
  • Increasing, Decreasing, and Constant
  • Domain
• Section 2.4
  • Standard Form
  • Slope
  • Properties
  • Secant Line
  • Business Models
• Section 2.5
  • Point-Slope Form
    • Examples
  • Horizontal and Vertical Lines
  • Parallel and Perpendicular Lines
    • Examples
• Section 2.6
  • Continuity
  • Basic Graphs and Information
• Section 2.7
  • Definitions
    • Stretch or Shrink
    • Reflecting
    • Vertical or Horizontal Translations
  • Examples
• Section 2.8
  • Basic Operations
  • Difference Quotient
    • Examples
  • Composition of Functions

Chapter 3:

• Section 3.1
  • Definitions
  • Vertex Formula
    • Example of Vertex and Axis of Symmetry
    • \(x\) and \(y\) Intercepts
  • Free Fall Model
• Section 3.2
  • Real Number Division Algorithm
  • Division Algorithm for Polynomials
  • Synthetic Division
    • Synthetic Division Examples
  • Remainder Theorem
  • Root (or Zero) of a Function
• Section 3.3
  • Factor Theorem and Rational Zero Theorem
    • Example(s)
  • Fundamental Theorem of Algebra and Number of Zeros Theorem
  • Complex Numbers
• Section 3.4
• Section 3.5

Chapter 4:

• Section 4.1
• Section 4.2
• Section 4.3
  • Definition and Properties
  • Examples
• Section 4.4
• Section 4.5
  • Solve Exponential Equations
  • Solve Logarithmic Equations
• Section 4.6
  • Exponential Growth Model
  • Exponential Decay Model
  • Exponential Find \(k\)
  • Newton’s Law of Cooling

Chapter 5:

• Section 5.1
  • Two-by-Two System of Linear Equations
  • Three-by-Three System of Linear Equations
• Section 5.2
  • Two by Two Examples
  • Three by Three Examples
  • Two by Three Example
• Section 5.3
  • Two by Two Determinant Example(s)
  • Three by Three Determinant Example(s)
  • Determinant Theorems
  • Cramer’s Rule
• Section 5.5
• Section 5.7
  • Multiplication
• Section 5.8

Chapter 6:

• Section 6.1
• Section 6.2
• Section 6.3
• Section 6.4

Chapter 7:

• Section 7.1
• Section 7.2
  • Sequence
  • Series
• Section 7.3
  • Sequence
  • Series
  • Future Value of an Annuity