Course Contents at a Glance
The following list shows a summary of the topics covered in this course. To see all of the course pages, visit the Table of Contents.Module 1: Functions and Function Notation
- Determine whether a relation represents a function
- Find the input and output values of a function
- Determine whether a function is one-to-one
- Use the vertical line test to identify functions
- Graph the functions listed in the library of functions
Module 2: Domain and Range
- Find the domain of a function defined by an equation
- Use notations to specify domain and range
- Find domain and range from graphs
- Find domains and ranges of the toolkit functions
- Graph piecewise-defined functions
Module 3: Rates of Change and Behavior of Graphs
- Find the average rate of change of a function
- Use a graph to determine where a function is increasing, decreasing, or constant
- Use a graph to locate the absolute maximum and absolute minimum
Module 4: Composition of Functions
- Combine functions using algebraic operations
- Create a new function by composition of functions
- Evaluate composite functions
- Find the domain of a composite function
- Decompose a composite function into its component functions
Module 5: Transformation of Functions
- Graph functions using vertical and horizontal shifts
- Graph functions using reflections about the x-axis and the y-axis
- Determine whether a function is even, odd, or neither from its graph
- Graph functions using compressions and stretches
- Combine vertical and horizontal shifts
Module 6: Absolute Value Functions
- Graph an absolute value function
- Solve an absolute value equation
- Solve an absolute value inequality
Module 7: Inverse Functions
- Verify inverse functions
- Determine the domain and range of an inverse function
- Find or evaluate the inverse of a function
- Use the graph of a function to graph its inverse
Module 8: Linear Functions
- Represent a linear function
- Determine whether a linear function is increasing, decreasing, or constant
- Calculate and interpret slope
- Write the point-slope form of an equation
- Write and interpret a linear function
Module 9: Graphs of Linear Functions
- Graph linear functions
- Write the equation for a linear function from the graph of a line
- Given the equations of two lines, determine whether their graphs are parallel or perpendicular
- Write the equation of a line parallel or perpendicular to a given line
- Solve a system of linear equations
Module 10: Modeling with Linear Functions
- Identify steps for modeling and solving
- Build linear models
- Build systems of linear models
Module 11: Fitting Linear Models to Data
- Draw and interpret scatter plots
- Find the line of best fit
- Distinguish between linear and nonlinear relations
- Use a linear model to make predictions
Module 12: Complex Numbers
- Express square roots of negative numbers as multiples of i
- Plot complex numbers on the complex plane
- Add and subtract complex numbers
- Multiply and divide complex numbers
Module 13: Quadratic Functions
- Recognize characteristics of parabolas
- Understand how the graph of a parabola is related to its quadratic function
- Determine a quadratic function’s minimum or maximum value
- Solve problems involving a quadratic function’s minimum or maximum value
Module 14: Power Functions and Polynomial Functions
- Identify power functions
- Identify end behavior of power functions
- Identify polynomial functions
- Identify the degree and leading coefficient of polynomial functions
Module 15: Graphs of Polynomial Functions
- Recognize characteristics of graphs of polynomial functions
- Use factoring to find zeros of polynomial functions
- Identify zeros and their multiplicities
- Determine end behavior
- Understand the relationship between degree and turning points
- Graph polynomial functions
- Solving Polynomial Inequalities
- Use the Intermediate Value Theorem
Module 16: Dividing Polynomials
- Use long division to divide polynomials
- Use synthetic division to divide polynomials
- Use polynomial division to solve application problems
Module 17: Zeros of Polynomial Functions
- Evaluate a polynomial using the Remainder Theorem
- Use the Factor Theorem to solve a polynomial equation
- Use the Rational Zero Theorem to find rational zeros
- Find zeros of a polynomial function
- Use the Fundamental Theorem of Algebra
- Use the Linear Factorization Theorem to find polynomials with given zeros
- Use Descartes’ Rule of Signs
- Solve real-world applications of polynomial equations
Module 18: Rational Functions
- Use arrow notation
- Solve applied problems involving rational functions
- Find the domains of rational functions
- Identify vertical asymptotes
- Identify horizontal asymptotes
- Graph rational functions
Module 19: Inverses and Radical Functions
- Find the inverse of a polynomial function
- Restrict the domain to find the inverse of a polynomial function
Module 20: Modeling Using Variation
- Solve direct variation problems
- Solve inverse variation problems
- Solve problems involving joint variation
Module 21: Exponential Functions
- Evaluate exponential functions
- Find the equation of an exponential function
- Use compound interest formulas
- Evaluate exponential functions with base e
Module 22: Graphs of Exponential Functions
- Graph exponential functions
- Graph exponential functions using transformations
Module 23: Logarithmic Functions
- Convert from logarithmic to exponential form
- Convert from exponential to logarithmic form
- Evaluate logarithms
- Use common logarithms
- Use natural logarithms
Module 24: Graphs of Logarithmic Functions
- Identify the domain of a logarithmic function
- Graph logarithmic functions
- Graphing Transformations of Logarithmic Functions
Module 25: Logarithmic Properties
- Use the product rule for logarithms
- Use the quotient and power rules for logarithms
- Expand logarithmic expressions
- Condense logarithmic expressions
- Use the change-of-base formula for logarithms
Module 26: Exponential and Logarithmic Equations
- Use like bases to solve exponential equations
- Use logarithms to solve exponential equations
- Use the definition of a logarithm to solve logarithmic equations
- Use the one-to-one property of logarithms to solve logarithmic equations
- Solve applied problems involving exponential and logarithmic equations
Module 27: Exponential and Logarithmic Models
- Model exponential growth and decay
- Use Newton’s Law of Cooling
- Use logistic-growth models
- Choose an appropriate model for data
Module 28: Fitting Exponential Models to Data
- Build an exponential model from data
- Build a logarithmic model from data
- Build a logistic model from data
Module 29: Systems of Linear Equations: Two Variables
- Solving Systems of Equations by Graphing
- Solving Systems of Equations by Substitution
- Solving Systems of Equations in Two Variables by the Addition Method
- Identifying and Expressing Solutions to Systems of Equations
- Using Systems of Equations to Investigate Profits
Module 30: Systems of Linear Equations: Three Variables
- Solving Systems of Three Equations in Three Variables
- Inconsistent and Dependent Systems in Three Variables
Module 31: Matrices and Matrix Operations
- Finding the Sum and Difference of Two Matrices
- Finding Scalar Multiples of a Matrix
- Finding the Product of Two Matrices
Module 32: Solving Systems with Gaussian Elimination
- The Augmented Matrix of a System of Equations
- Performing Row Operations on a Matrix
- Solving a System of Linear Equations Using Matrices
Module 33: Solving Systems with Inverses
- Finding the Inverse of a Matrix
- Solving a System of Linear Equations Using the Inverse of a Matrix
Module 34: Sequences and Their Notations
- Writing the Terms of a Sequence Defined by an Explicit Formula
- Investigating Alternating Sequences
- Investigating Explicit Formulas
- Writing the Terms of a Sequence Defined by a Recursive Formula
Module 35: Arithmetic Sequences
- Finding Common Differences
- Using Formulas for Arithmetic Sequences
- Finding the Number of Terms in a Finite Arithmetic Sequence
Module 36: Geometric Sequences
- Finding Common Ratios
- Writing Terms of Geometric Sequences
- Solving Application Problems with Geometric Sequences
Module 37: Series and Their Notations
- Using Summation Notation
- Using the Formula for Arithmetic Series
- Using the Formula for Geometric Series
- Finding Sums of Infinite Series
- Solving Annuity Problems
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