https://courses.vccs.edu/colleges/svcc/courses/MTH161-PreCalculusI

Effective: 2023-05-01

Course Description

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 and UCGS transfer course.
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

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 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))
  • 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