Pre-Calculus: Math 111
Chapter 1: Graphs
1.1 Rectangular Coordinates, Graphing Utilities, Introduction to Graphing Equations
Graph Equations by hand by plotting points
Use a Graphing Utility to Graph Equations, Create Tables, and to Approximate Intercepts
1.2 Intercepts, Symmetry, Graphing Key Equations
Finding intercepts Algebraically from an Equation
Test an Equation for Symmetry with Respect to the x-axis, y-axis, and the Origin
Identifying Graphs of Key Equations
1.3 Solving Equations Using a Graphing Utility
Solve Equations Using a Graphing Utility
1.4 Lines
Calculate and Interpret the Slope of a Line
Graph Lines Given a Point and the Slope
Find the Equation of a Vertical Line
Use the Point-Slope Form of a Line; Identify Horizontal Lines
Write the Equation of a Line in Slope-Intercept Form
Identify the Slope and y-Intercept of a Line from Its Equation
Graph Lines Written in General Form Using Intercepts
Find Equations of Perpendicular Lines
1.5 Circles
Write the stand form of the equation of a circle
Graph a Circle by Hand and by using a graphing utility
Chapter 2: Functions and Their Graphs
2.1: Functions
Determine Whether a Relation Represents a Function
Find the Domain of a Function Defined by an Equation
Form the Sum and Difference of Two Functions
Form the Product and Quotient of Two Functions
2.2 The graph of a Function
Identify the Graph of a Function
2.3 Properties of Functions
Determine Even and Odd Functions from a Graph
Identify Even and Odd Functions from the Equation
Use a Graph to Determine Where a Function is Increasing, Decreasing, or Constant
Use a Graph to Locate Local Maxima and Local Minima
Find the Average Rate of Change of a Function
2.4 Library of Functions; Piecewise-defined Functions
Graph the Functions Listed in the Library of Functions
Graph Piecewise-defined Functions
2.5 Graphing Techniques: Transformations
Graph Functions Using Vertical and Horizontal Shifts
Graph Functions Using Compressions and Stretches
Graph Functions Using Reflections about the x-Axis and y-Axis
2.6 Mathematical Models: Building Functions
Chapter 3: Linear and Quadratic Functions
3.1 Linear Functions, Their Properties, and Linear Models
Use Average Rate of Change to Identify Linear Functions
Determine Whether a Linear function is Increasing, Decreasing, or Constant
Build Linear Models from Verbal Descriptions
3.2 Building Linear Models from Data
Draw and Interpret Scatter Diagrams
Use a Graphing Utility to Find the Line of Best Fit
3.3 Quadratic Functions and Their Properties
Graph a Quadratic Function Using Transformations
Identify the Vertex and Axis of Symmetry of a Quadratic Function
Graph a Quadratic Function Using Its Vertex, Axis, and Intercepts
Find the Maximum or Minimum Value of a Quadratic Function
3.4 Building Quadratic Models from Verbal Descriptions and from Data
Build Quadratic Models from Data
3.5 Inequalities Involving Quadratic Functions
Solving Inequalities Involving a Quadratic Function
Chapter 4: Polynomial and Rational Functions
4.1 Polynomial Functions and Models
Identify Polynomial Functions and Their Degree
Graph Polynomial Functions Using Transformations
Identify the Real Zeros of a Polynomial Function and Their Multiplicity
Analyze the Graph of a Polynomial Function
4.2 Properties of Rational Functions
Find the Domain of a Rational Function
Find the Vertical Asymptotes of a Rational Function
Find the Horizontal or Oblique Asymptotes of a Rational Function
4.3 The Graph of a Rational Function
Analyze the Graph of a Rational Function
Solve Applied Problems Involving Rational Functions
4.4 Polynomial and Rational Inequalities
Solve Polynomial Inequalities Algebraically and Graphically
Solve Rational Inequalities Algebraically and Graphically
4.5 The Real Zeros of Polynomial Function
Use the Rational Zeros Theorem to List the Potential Rational Zeros of a Polynomial Function
Find the Real Zeros of a Polynomial Function
Use the Theorem for Bounds on Zeros
Use the Intermediate Value Theorem
4.6 Complex Zeros; Fundamental Theorem of Algebra
Use the Conjugate Pairs Theorem
Find a Polynomial Function with Specified Zeros
Find the Complex Zeros of a Polynomial Function
Chapter 5: Exponential and Logarithmic Functions
5.1 Composite Functions
Find the Domain of a Composite Function
5.2 One-to-One Functions; Inverse Functions
Determine Whether a Function is One-to-One
Determine the Inverse of a Function Defined by a Map or a Set of Ordered Pairs
Obtain the Graph of the Inverse Function from the Graph of the Function
Find the Inverse of a Function Defined by an Equation
5.3 Exponential Functions
Sketching Exponential Functions and Their Transformations
Laws of Exponents and Solving Basic Exponential Equations
Modeling the Equation of an Exponential Function Using Two Ordered Pairs
Solve Exponential Equations and Exponential Functions
5.4 Logarithmic Functions
Evaluate Logarithmic Expressions
Determine the Domain of a Logarithmic Function
5.5 Properties of Logarithms
Work with the Properties of Logarithms
Write a Logarithmic Expression as a Single Logarithm
Evaluate Logarithms Whose Base Is Neither 10 nor e
5.6 Logarithmic and Exponential Equations
Exponential and Logarithmic Equations
Solve Exponential Equations with Logarithms
Solve Logarithmic and Exponential Equations Using a Graphing Utility
5.7 Financial Models
Calculate Effective Rates of Return
Determine the Present Value of a Lump Sum of Money
Determine the Rate of Interest or Time Required to Double a Lump Sum of Money
5.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
Exponential Growth and Decay Models
5.9 Build Exponential, Logarithmic, and Logistic Models from Data
12: Induction; The Binomial Theorem
12.1 Sequences
12.2 Arithmetic Sequences
Finding Arithmetic Sequences and Series
Find the Sum of a Finite Arithmetic Sequence
12.3 Geometric Sequences; Geometric Series
Finding and solving a formula for a geometric sequence
12.4 Mathematical Induction
Proving an Expression for the Sum of All Positive Integers Up to and Including n by Induction
12.5 The Binomial Theorem