Revised 08/2021

MDE 61 - Learning Support for Pre-calculus (3 CR.)

Course Description

Provides support to ensure success for students co-enrolled in Pre-Calculus (MTH 161). Course will review foundational topics through direct instruction, guided practice, and individualized support. Lecture 3 hours. Total 3 hours per week.

General Course Purpose

This course provides support to ensure student success with the MTH 161 objectives.

Course Prerequisites/Corequisites

Prerequisite: MTH 161 with MDE 61 is any six MTE units 1-9, MDE 60, or other placement methods.

Course Objectives

Relations and Functions
  • Distinguish between relations and functions.
  • Evaluate functions both numerically and algebraically.
  • Determine the domain and range of functions in general, including root and rational functions.
  • Perform arithmetic operations on functions, including the composition of functions and the difference quotient.
  • Identify and graph linear, absolute value, quadratic, cubic, and square root functions, and their transformations.
  • Determine and verify inverses of one-to-one functions.
Polynomial and Rational Functions
  • Determine the general and standard forms of quadratic functions.
  • Use formula and completing the square methods to determine the standard form of a quadratic function.
  • Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions.
  • Identify zeros (real-valued roots) and complex roots and determine end behavior of higher order polynomials and graph the polynomial, and graph.
  • Determine if a function demonstrates even or odd symmetry.
  • Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers.
  • Identify intercepts, end behavior, and asymptotes of rational functions, and graph.
  • Solve polynomial and rational inequalities.
  • Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and inequality of functions (f(x) > g(x))
  • Decompose partial fractions of the form P(x)/Q(x) where Q(x) is a product of linear factors.
 Exponential and Logarithmic Functions
  • Identify and graph exponential and logarithmic functions and their transformations.
  • Use properties of logarithms to simplify and expand logarithmic expressions.
  • Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms.
  • Solve exponential and logarithmic equations using one-to-one and inverse properties.
  • Solve application problems involving exponential and logarithmic functions.
Systems of Equations
  • Solve three variable linear systems of equations using the Gaussian elimination method.

Major Topics to Be Included

  • Factoring
  • Simplifying algebraic expressions
  • Solving higher order equations with real and complex roots
  • Graphing
  • Asymptotic behavior
  • Power, polynomial, rational, exponential, and logarithmic functions
  • Systems of equations and inequalities
  • Inverse functions
  • Difference quotient
  • Gaussian elimination