Math 1021 College Algebra provides an in-depth treatment of solving equations and inequalities; function properties and graphs; inverse functions; linear, quadratic, polynomial, rational, exponential and logarithmic functions with applications; systems of equations.
Topics and Objectives
Linear Equations
Recognizing linear equations
Solving linear equations with integer coefficients
Solving linear equations involving fractions
Solving linear equations involving decimals
Recognizing rational equations
Solving rational equations that lead to linear equations
Quadratic Equations
Solving quadratic equations by factoring and the zero product property
Solving quadratic equations using the square root property
Solving quadratic equations using the quadratic formula
Using the discriminant to determine the type of solutions of a quadratic equation
Other Types of Equations
Solving higher-order polynomial equations
Solving equations that are quadratic in form
Solving equations involving single radicals
Linear Inequalities
Solving linear inequalities
Solving three-part inequalities
Absolute Value Equations and Inequalities
Solving an absolute value equation
Solving an absolute value “less than” inequality
Solving an absolute value “greater than” inequality
The Rectangular Coordinate System
Plotting ordered pairs
Finding intercepts of a graph given an equation
Finding the midpoint of a line segment using the midpoint formula
Finding the distance between two points using the distance formula
Circles
Writing the standard form of an equation of a circle
Sketching the graph of a circle
Converting the general form of a circle into standard form
Lines
Determining the slope of a line
Sketching a line given a point and the slope
Finding the equation of a line using the point-slope form
Finding the equation of a line using the slope-intercept form
Writing the equation of a line in standard form
Finding the slope and the y-intercept of a line in standard form
Sketching lines by plotting intercepts
Finding the equation of a horizontal line and a vertical line
Parallel and Perpendicular Lines
Understanding the definition of parallel lines
Understanding the definition of perpendicular lines
Determining whether two lines are parallel, perpendicular, or neither
Finding the equations of parallel and perpendicular lines
Relations and Functions
Understanding the definitions of relations and functions
Determining whether equations represent functions
Using function notation; evaluating functions
Using the vertical line test
Determining the domain of a function given the equation
Properties of a Function’s Graph
Determining the intercepts of a function
Determining the domain and range of a function from its graph
Determining whether a function is increasing, decreasing, or constant
Determining relative maximum and relative minimum values of a function
Determining whether a function is even, odd, or neither
Determining information about a function from a graph
Graphs of Basic Functions; Piecewise Functions
Sketching the graphs of the basic functions
Sketching the graphs of basic functions with restricted domains
Analyzing piecewise-defined functions
Transformations of Functions
Using vertical shifts to graph functions
Using horizontal shifts to graph functions
Using reflections to graph functions
Using vertical stretches and compressions to graph functions
Using combinations of transformations to graph functions
Composite Functions
Forming and evaluating composite functions
Determining the domain of composite functions
One-to-One Functions; Inverse Functions
Understanding the definition of a one-to-one function
Determining whether a function is one-to-one using the horizontal line test
Understanding and verifying inverse functions
Sketching the graphs of inverse functions
Finding the inverse of a one-to-one function
Quadratic Functions
Understanding the definition of a quadratic function and its graph
Graphing quadratic functions written in vertex form
Graphing quadratic functions using the vertex formula
Determining the equation of a quadratic function given its graph
Applications and Modeling of Quadratic Functions
Maximizing projectile motion functions
Maximizing functions in economics
The Graphs of Polynomial Functions
Understanding the definition of a polynomial function
Sketching the graphs of power functions
Determining the end behavior of polynomial functions
Determining the intercepts of a polynomial function
Determining the real zeros of polynomial functions and their multiplicities
Sketching the graph of a polynomial function
Determining a possible equation of a polynomial function given its graph
Rational Functions and Their Graphs
Finding the domain and intercepts of rational functions
Identifying vertical asymptotes
Identifying horizontal asymptotes
Using transformations to sketch the graphs of rational functions
Finding removable discontinuities, intercepts, asymptotes and sketch graphs of rational functions
Exponential Functions
Understanding the characteristics of exponential functions
Sketching the graphs of exponential functions using transformations
Solving exponential equations by relating the bases
Solving applications of exponential functions
Logarithmic Functions
Understanding the definition of a logarithmic function
Evaluating logarithmic expressions
Understanding the properties of logarithms
Using the common and natural logarithms
Understanding the characteristics of logarithmic functions
Sketching the graphs of logarithmic functions using transformations
Finding the domain of logarithmic functions
Properties of Logarithms
Using the product rule, quotient rule, and power rule for logarithms
Expanding and condensing logarithmic expressions
Solving logarithmic equations using the logarithm property of equality
Using the change of base formula
Exponential and Logarithmic Equations
Solving exponential equations
Solving logarithmic equations
Applications of Exponential and Logarithmic Functions
Solving compound interest applications
Solving exponential growth and decay applications
Systems of Equations
Verifying solutions to a system of linear equations in two variables
Solving a system of linear equations using the substitution method
Solving a system of linear equations using the elimination method
Solving applied problems using a system of linear equations