# College Algebra (OpenStax)

MindEdge has enhanced OpenStax’s College Algebra learning resource, which exposes students to topics in algebra. Students explore the mathematics while simultaneously applying this knowledge to real-world scenarios. Students solve various problems through the lens of a statistician, using a variety of tools to develop solutions. The course includes pretests and self-assessments, interactive exercises, graphics, and games that appeal to a variety of learning styles. Open ended questions that apply topics to real world problems give students opportunities to apply critical thinking skills to real-world mathematics scenarios.

MindEdge has enhanced OpenStax courses with interactive games, video commentary, adaptive learning segments, additional practice questions, and a robust question database.

## Module 1: Learning Outcomes

• Determine whether a relation represents a function
• Find the value 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
• Graph functions using vertical and horizontal shifts
• Graph functions using reflections about the x-axis axis and the y-axis
• Determine whether a function is even, odd, or neither from its graph
• Graph functions using compressions and stretches
• Combine transformations
• Graph an absolute value function
• Solve an absolute value equation
• Verify inverse functions
• Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
• Find or evaluate the inverse of a function
• Use the graph of a one-to-one function to graph its inverse function on the same axes
• Represent a linear function
• Determine whether a linear function is increasing, decreasing, or constant
• Interpret slope as a rate of change
• Write and interpret an equation for a linear function
• Graph linear functions
• Determine whether lines are parallel or perpendicular
• Write the equation of a line parallel or perpendicular to a given line
• Build linear models from verbal descriptions
• Model a set of data with a linear function.

## Module 2: Learning Outcomes

• 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
• Identify power functions
• Identify end behavior of power functions
• Identify polynomial functions
• Identify the degree and leading coefficient 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
• Use the Intermediate Value Theorem
• 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 Linear Factorization Theorem to find polynomials with given zeros
• Use Descartes’ Rule of Signs
• Solve real-world applications of polynomial equation
• Use arrow notation
• Solve applied problems involving rational functions
• Find the domains of rational functions
• Identify vertical asymptotes
• Identify horizontal asymptotes
• Graph rational functions
• Find the inverse of an invertible polynomial function
• Restrict the domain to find the inverse of a polynomial function.

## Module 3: Learning Outcomes

• Evaluate exponential functions
• Find the equation of an exponential function
• Use compound interest formulas
• Evaluate exponential functions with base e
• Graph exponential functions
• Graph exponential functions using transformations
• Convert from logarithmic to exponential form
• Convert from exponential to logarithmic form
• Evaluate logarithms
• Use common logarithms
• Use natural logarithms
• Identify the domain of a logarithmic function
• Graph logarithmic functions
• Use the product rule for logarithms
• Use the quotient rule for logarithms
• Use the power rule for logarithms
• Expand logarithmic expressions
• Condense logarithmic expressions
• Use the change-of-base formula for logarithms
• 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
• Model exponential growth and decay
• Use Newton’s Law of Cooling
• Use logistic-growth models
• Choose an appropriate model for data
• Express an exponential model in base e

## Module 4: Learning Outcomes

• Write the terms of a sequence defined by an explicit formula
• Write the terms of a sequence defined by a recursive formula
• Use factorial notation
• Find the common difference for an arithmetic sequence
• Write terms of an arithmetic sequence
• Use a recursive formula for an arithmetic sequence
• Use an explicit formula for an arithmetic sequence
• Find the common ratio for a geometric sequence
• List the terms of a geometric sequence
• Use a recursive formula for a geometric sequence
• Use an explicit formula for a geometric sequence
• Use summation notation
• Use the formula for the sum of the first n terms of an arithmetic series
• Use the formula for the sum of the first n terms of a geometric series
• Use the formula for the sum of an infinite geometric series
• Solve annuity problems
• Solve counting problems using the Addition Principle
• Solve counting problems using the Multiplication Principle
• Solve counting problems using permutations involving n distinct objects
• Solve counting problems using combinations
• Find the number of subsets of a given set
• Solve counting problems using permutations involving n non-distinct objects
• Apply the Binomial Theorem
• Construct probability models
• Compute probabilities of equally likely outcomes
• Compute probabilities of the union of two events
• Use the complement rule to find probabilities
• Compute probability using counting theory.

## Module 5: Learning Outcomes

• Solve systems of three equations in three variables
• Identify inconsistent systems of equations containing three variables
• Express the solution of a system of dependent equations containing three variables
• Solve systems of equations by graphing
• Solve systems of equations by substitution
• Solve systems of equations by addition
• Identify inconsistent systems of equations containing two variables
• Express the solution of a system of dependent equations containing two variables
• Find the sum and difference of two matrices
• Find scalar multiples of a matrix
• Find the product of two matrices
• Write the augmented matrix of a system of equations
• Write the system of equations from an augmented matrix
• Perform row operations on a matrix
• Solve a system of linear equations using matrices
• Find the inverse of a matrix
• Solve a system of linear equations using an inverse matrix
• Evaluate 2 × 2 determinants
• Use Cramer’s Rule to solve a system of equations in two variables
• Evaluate 3 × 3 determinants
• Use Cramer’s Rule to solve a system of three equations in three variables
• Know the properties of determinants.