### Math 1100: College Algebra

#### Course Description:

A review of exponents, order of operations, factoring, and simplifying polynomial, rational, and radical expressions. Topics include: linear, quadratic, polynomial, rational, inverse, exponential, and logarithmic functions and their applications. Students will solve equations involving these functions, and systems of linear equations in two variables, as well as inequalities.

#### Textbook and Course materials:

• MML AUTO ACCESS - Required
• COURSE WORKBOOK – Custom Edition - Required – A manual containing an outline of class notes.
• TEXTBOOK – Recommended - College Algebra, 5th edition, by Beecher, Penna, and Bittinger.

#### Sections Covered

• JiT Just in Time
• A review of The Real Number System; Integer Exponents and Order of Operations; Addition, Subtractions, and Multiplication of Polynomials; Factoring; The Basics of Equation Solving; Rational Expressions; Radical Notation and Rational Exponents
• Section 1.1  Introduction to Graphing
• Plot points
• Determine whether an ordered pair is a solution of an equation
• Find the x- and y-intercepts of an equation of the form
• Graph equations
• Find the distance between two points in the plane and find the midpoint of a segment
• Find an equation of a circle with a given center and radius, and given an equation of a circle in standard form, find the center and the radius
• Graph equations of circles
• 1.2  Functions and Graphs
• Determine whether a correspondence or a relation is a function
• Find function values, or outputs, using a formula or a graph
• Graph functions
• Determine whether a graph is that of a function
• Find the domain and the range of a function
• Solve applied problems using functions
• 1.3  Linear Functions
• Determine the slope of a line given two points on the line
• Solve applied problems involving slope, or average rate of change
• Find the slope and the y-intercept of a line given the equation  or
• Graph a linear equation using the slope and the y-intercept
• Solve applied problems involving linear functions
• 1.4  Equations of Lines
• Determine equations of lines
• Given the equations of two lines, determine whether their graphs are parallel or perpendicular
• Model a set of data with a linear function
• 1.5  Linear Equations, Functions, Zeros, and Applications
• Solve linear equations
• Solve applied problems using linear models
• Find zeros of linear functions
• 1.6  Solving Linear Inequalities
• Solve linear inequalities
• Solve compound inequalities
• Solve applied problems using inequalities
• 2.1  Increasing, Decreasing, and Piecewise Functions
• Graph functions, looking for intervals on which the function is increasing, decreasing, or constant, and estimate relative maxima and minima
• Given an application, find a function that models the application. Find the domain of the function and function values
• Graph functions defined piecewise
• 2.2  The Algebra of Functions
• Find the sum, the difference, the product, and the quotient of two functions, and determine the domains of the resulting functions
• Find the difference quotient for a function
• 2.3  The Composition of Functions
• Find the composition of two functions and the domain of the composition
• Decompose a function as a composition of two functions
• 2.4  Symmetry
• Determine whether a graph is symmetric with respect to the x-axis, the y-axis, and the origin
• Determine whether a function is even, odd, or neither even nor odd
• 2.5  Transformations
• Given the graph of a function, graph its transformation under translations, reflections, stretching, and shrinking
• 2.6 Variation and Applications
• Find equations of direct variation, inverse variation, and combined variation given values of the variables
• Solve applied problems involving variation
• 3.1  The Complex Numbers
• Perform computations involving complex numbers
• 3.2  Quadratic Equations, Functions, Zeros, and Models
• Find zeros of quadratic functions and solve quadratic equations by using the principle of zero products, by using the principle of square roots, by completing the square, and by using the quadratic formula
• Solve equations that are reducible to quadratic
• Solve applied problems using quadratics equations
• 3.3  Analyzing Graphs of Quadratic Functions
• Find the vertex, the axis of symmetry, and the maximum or minimum value of a quadratic function using the method of completing the square
• Solve applied problems involving maximum and minimum function values
• 3.4  Solving Rational Equations and Radical Equations
• Solve rational equations
• 3.5  Solving Equations and Inequalities with Absolute Value
• Solve equation with absolute value
• Solve inequalities with absolute value
• 4.1  Polynomial Functions
• Determine the behavior of the graph of a polynomial function using the leading-term test
• Factor polynomial functions and find their zeros and their multiplicity
• Solve applied problems using polynomial models
• 4.2  Graphing Polynomial Functions
• Graph polynomial functions
• Use the intermediate value theorem to determine whether a function has a zero between two given real numbers
• 4.5  Rational Functions
• For a rational function, find the domain and graph the function, identifying all of the asymptotes
• Solve applied problems involving rational functions
• 4.6  Polynomial Inequalities and Rational Inequalities
• Solve polynomial inequalities
• Solve rational inequalities
• 5.1  Inverse Functions
• Determine whether a function is one-to-one, and if it is, find a formula for its inverse
• Simplify expressions of the type  and
• 5.2  Exponential Functions
• Graph exponential equations and exponential functions
• Solve applied problems involving exponential functions and their graphs
• 5.3  Logarithmic Functions
• Find common logarithms and natural logarithms with and without a calculator
• Convert between exponential equations and logarithmic equations
• Change logarithmic bases
• Graph logarithmic functions
• Solve applied problems involving logarithmic functions
• 5.4  Properties of Logarithmic Functions
• Convert from logarithms of products, powers, and quotients to expressions
• Simplify expressions of the type  and
• 5.5  Solving Exponential Equations and Logarithmic Equation
• Solve exponential equations
• Solve logarithmic equations
• 6.1  Systems of Equations in Two Variables
• Solve a system of two linear equations in two variables by graphing
• Solve a system of two linear equations in two variables using the substitution method and the elimination method
• Use systems of two linear equations to solve applied problems
• 6.2  Systems of Equations in Three Variables
• Solve systems of linear equations in three variables
• Use systems of three equations to solve applied problems
• Model a situation using a quadratic function
• 6.7  Systems of Inequalities
• Graph linear inequalities
• Graph systems of linear inequalities
• Solve linear programming problems