## Learning Support for Pre-Calculus - MDE 61 at Tidewater Community College

https://courses.vccs.edu/colleges/tcc/courses/MDE61-LearningSupportforPreCalculus

Effective: 2020-01-01

### 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.
3 credits

The course outline below was developed as part of a statewide standardization process.

### General Course Purpose

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

### Course Prerequisites/Corequisites

Corequisite: MTH 161

### 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

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