Mar 28, 2024  
2021-22 Catalog 
    
2021-22 Catalog [ARCHIVED CATALOG]

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MATH& 141 - Pre Calculus I

5 Credits


Prepares students for the calculus sequence. Real-valued functions, including techniques for graphing polynomial, rational, piecewise, exponential, and logarithmic functions. Also includes circles, basic function properties, nonlinear inequalities, and complex numbers.

Pre-requisite(s) MATH 098 min 2.0

 
Placement Eligibility Math 141
Course Note Graphing Calculator Required; TI-84 recommended
Fees

Quarters Typically Offered
Summer Day
Fall Day, Evening, Online
Winter Day, Evening
Spring Day, Evening

Designed to Serve Transfer students in mathematics, engineering and the sciences
Active Date 20170622T08:38:37

Grading System Decimal Grade
Class Limit 32
Contact Hours: Lecture 55 Lab 0 Worksite 0 Clinical 0 Other 0
Total Contact Hours 55
Degree Distributions:
AA

  • Quantitative Skills
  • Science

ProfTech Related Instruction
  • Computation


PLA Eligible Yes

Course Outline
The course is organized into five strands:

I. Algebra:

  • Solve nonlinear inequalities (polynomial and rational) using sign analysis and express solutions using interval notation and understand the relationship between sign charts and graphs of functions.
  • Put the general equation of a circle into standard form and sketch graph.
  • Solve various types of equations: 
    • Quadratic equations
    • Rational equations
    • Polynomial equations
    • Exponential equations
    • Logarithmic equations
  • Combine and expand logarithmic expressions using the properties of logs.
  • Solve equations algebraically using properties of exponents and logarithms.
  • Perform long division and synthetic division of polynomials.

II. Functions-with an emphasis on piecewise, rational, polynomial, exponential, and logarithmic functions.

  • For limited types of elementary functions be able to use and interpret functional notation.
  • Determine the domain and range of a variety of functions algebraically and graphically.
  • Determine the difference quotient for polynomial and rational functions.
  • Determine the absolute and/or local extrema for elementary functions.
  • Use simple transformations (horizontal, vertical, x & y-axis rotations) to create graphs of new functions from their basic elementary functions.
  • Determine intervals where a function is increasing/decreasing/constant emphasis put on polynomial, rational, piecewise, exponential, and logarithms.
  • Algebraically construct new functions using addition, subtraction, multiplication, division, and composition (as well as simplifying the result).
  • Determine and interpret the average rate of change in a function.
  • For rational functions a student will be able to:
    • calculate x and y intercepts
    • calculate horizontal, vertical, and oblique asymptotes
    • calculate holes
    • sketch the graph o determine the domain and range
  • For polynomial functions a student will be able to:
    • sketch or describe the possible shape of a polynomial function of degree n including:
      • 1. the number of turning points
      • 2. number of possible real and complex roots and be able to find them by factoring or rational root theorem
      • 3.  end behavior
      • 4. determine the domain and range
  • For piecewise functions a student will be able to: 
    • sketch by hand
    • determine the domain and range
    • identify various discontinuities
  • For logarithmic and exponential functions a student will be able to:
    • calculate any vertical/horizontal asymptotes
    • determine the domain and range
    • calculate any x or y intercepts

III. Communication

  • Summarize and interpret mathematical information from written formats.
  • Identify, extract, and organize critical information into mathematical symbols.
  • Clearly communicate steps using proper terminology, symbolization, and notation.
  • Demonstrate attention to detail-students will be able to analyze written material for errors and explain why they are incorrect.

IV. Problem solving

  • Create realistic mathematical models for applied problems involving exponential, logarithmic, and polynomial functions.
  • Create a suitable quadratic function for modeling a real world situation presented using words, data, or diagram.
  • Identify and justify whether a result generated from a model has real world significance.

V. Technology-emphasis on graphing calculator

  • Graph functions choosing the appropriate windows for viewing all details.
  • Effectively use the zoom in/out feature.
  • Use the calculator to find intercepts, points of intersection, and extrema for functions.
  • Use the table feature to determine values for functions.
  • Use the function feature on calculator to calculate multiple average rates of change.
  • Use a graphing calculator to evaluate logarithms of base 10 or e as well as utilizing the change of base formula.
  • Emphasize graphing rational, polynomial, logarithmic, and exponential functions.


Student Learning Outcomes
Recognize, describe, and analyze key features (domain, range, intercepts, holes, asymptotes) of important function families-polynomial, rational, piece-wise, exponential, and logarithmic functions.

Given the graphical or algebraic representation of a function a student will be able to state and sketch a transformation of the function and determine the domain and range of the transformed function.

Apply appropriate algebraic methods to find domain, intercepts, and asymptotes (where applicable) to a variety of functions including polynomial, rational, exponential, and logarithmic functions.

Identify and produce composite and inverse functions as well as graph a function and its inverse.

Identify key features of circles and sketch their graphs from equations in general and standard form.

Apply mathematical operations to solve polynomial, rational, exponential, and logarithmic equations.

Apply course concepts to solve real world problems.

Communicate, summarize, and interpret mathematical ideas in written and verbal form.

Effectively use graphing calculators to describe and graph circles and a variety of functions including rational, polynomial, exponential, and logarithmic functions.



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