LSU College of Science
LSU  | Mathematics

Math 1021 College Algebra Topics

Linear Equations

  • Recognizing linear equations
  • Solving linear equations with integer coefficients
  • Solving linear equations involving fractions
  • Solving linear equations involving decimals
  • Solving 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 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
  • 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 standard 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
  • Sketching 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