Dual Enrollment Program Support Course: Pre-Calculus

This support course (high school credit only) is designed to be taught in the fall semester preceding Math 1431 Business Calculus (dual enrollment) in the spring semester.

Topics & Objectives

Chapter and section numbers refer to Calculus for Business, Economics, Life, and Social Sciences, 14e (Barnett, Ziegler, Byleen).

Homework: Basic Number Concepts
  • Multiply and divide fractions
  • Add and subtract fractions
  • Simplify using order of operations
  • Graph inequalities on number lines and write them as intervals

Homework: Exponents and Radicals
  • Use properties of exponents
  • Simplify radicals
  • Use radicals and rational exponents

Homework: Linear Equations
  • Solve linear equations
  • Write linear equations
  • Graph linear equations
  • Solve systems of linear equations in two variables

Homework: Quadratic Equations
  • Factor trinomials
  • Solve quadratic equations using the square root property
  • Solve quadratic equations by factoring
  • Solve quadratic equations using the quadratic formula

Homework: Other Types of Equations
  • Solve equations with variable(s) in the denominator
  • Solve equations with radical
  • Solve equations of quadratic type

Homework: Functions: Domain, Range, and Evaluation
  • Determine whether sets, mappings, or tables define a function
  • Determine whether a graph defines a function
  • Find the domain and range of functions
  • Find function values from a graph
  • Evaluate functions
  • Find the average rate of change of a function, and graph the associated secant line
  • Find the difference quotient of a function

Homework: Functions: Properties of Functions
  • Find the domain of a function
  • Determine whether an equation defines a function and, if so, find the domain
  • Find the value of a function
  • Identify the graph of a function
  • Use a graph to find where a function is increasing, decreasing, or constant
  • Use a graph to find if a function is even or odd
  • Use a graph to locate local maxima and local minima
  • Find local maxima and minimum
  • Determine where a function is increasing or decreasing
  • Find the average rate of change of a function

Homework: Graphs of Basic Functions and Polynomials
  • Find the equation of lowest degree that has a given graph and intercepts
  • Analyze graphs of basic functions
  • Graph piecewise-defined functions
  • Graph and analyze quadratic functions
  • Sketch and analyze the graphs of polynomial functions
  • Describe the end behavior of the graph of a polynomial function
  • Factor polynomial functions and sketch their graphs
  • Find a polynomial function with real coefficients which satisfies given conditions

Homework: Functions: Transformations and Compositions
  • Graph functions using transformations
  • Find composite functions
  • Find the domain of composite functions
  • Decompose functions

Homework: Rational Expressions
  • Divide rational expressions using long division
  • Simplify rational expressions
  • Add and subtract rational expressions
  • Simplify complex rational expressions
  • Rationalize numerators and denominators

Homework: Rational Functions
  • Simplify complex rational expressions
  • Solve rational equations
  • Find equations of asymptotes and graph rational functions
  • Sketch graphs of rational functions and estimate function values

Homework: Exponential Functions
  • Graph exponential functions
  • Graph exponential functions using transformations
  • Use compound interest formulas
  • Write an exponential function for a given graph
  • Solve applications involving exponential functions

Homework: Logarithmic Functions
  • Evaluate logarithms using properties of logarithms
  • Evaluate logarithms using technology
  • Apply laws of logarithms to express as a sum, difference, and/or product
  • Apply laws of logarithms to express as a single logarithm
  • Solve exponential equations
  • Solve logarithmic equations

Homework: Common Algebra Applications in Calculus
  • Solve perimeter, area, and volume problems
  • Solve percent increase and percent decrease problems
  • Solve simple interest problems
  • Model exponential growth and decay