## MTH 161 - PreCalculus I at Southside Virginia Community College

### Course Description

Effective: 2019-08-01

Presents topics in power, polynomial, rational, exponential, and logarithmic functions, and systems of equations and inequalities. Credit will not be awarded for both MTH 161: Precalculus I and MTH 167: Precalculus with Trigonometry or equivalent. This is a Passport Transfer course.
Lecture 3 hours. Total 3 hours per week.
3 credits

### General Course Purpose

The general purpose of this one-semester course is to prepare students for a course in statistics or applied calculus sequence by providing them with the necessary competencies in algebra and functions. Precalculus I can also be applied in conjunction with Precalculus II in preparation for a course in calculus with analytic geometry.

### Course Prerequisites/Corequisites

Prerequisites: Competency in MTE 1-9 as demonstrated through placement or unit completion or equivalent or Corequisite: MCR 6: Learning Support for Precalculus I

### 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

• Relations and Functions
• Polynomial and Rational Functions
• Exponential and Logarithmic Functions
• Systems of Equations

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