College Algebra Syllabus and Course Outline Study Guide

Course Information

Overview

This document provides the syllabus and course outline for College Algebra (MATH-1314) at Temple College. It includes grading policies, required materials, important dates, and a detailed breakdown of topics covered throughout the semester.

Grading and EvaluationBest 3 of 4 Unit Tests: 40%

• Final Exam: 20%

Letter grades are assigned as follows:

Grading Scale

• Homework: 20%

• Five Quizzes: 20%

Grade	Percentage
A	90 to 100%
B	80 to 89.4%
C	70 to 79.4%
D	60 to 69.4%
F	Below 60%

Required Materials

• Textbook: College Algebra, 8th edition, by Robert F. Blitzer (ebook included with MyMathLab access)

• Calculator: Scientific or graphing calculator (TI-83, TI-84, TI-84+, or TI-Nspire recommended; no TI-89 or TI-92 models allowed)

• MyMathLab: Online platform for homework, quizzes, and tests

Course Schedule

Important Dates

Unit	Test Date	Final Exam
Unit 1 Test	Wednesday, September 30	Wednesday, November 19
Unit 2 Test	Wednesday, September 24
Unit 3 Test	Wednesday, October 15
Unit 4 Test	Wednesday, November 5

Course Outline & Content

Chapter Two – Functions and Their Graphs

• Basic Functions and Their Graphs

• Linear Functions and Their Graphs

• Quadratic Functions and Their Graphs

• Polynomial Functions; Composite Functions

• Inverse Functions

• Zeroes of Functions

Chapter Three – Polynomial and Rational Functions

• Graphing Polynomial Functions

• Dividing Polynomials and the Remainder and Factor Theorems

• Rational Functions and Their Graphs

Chapter Four – Exponential and Logarithmic Functions

• Exponential Functions

• Logarithmic Functions

• Properties of Logarithms

• Exponential and Logarithmic Equations

• Exponential Growth & Decay; Modeling Data

Chapter Six – Matrices and Linear Systems

• Gaussian & Gauss-Jordan Elimination

• Matrix Operations

• Determinants

• Inverse Matrices

• Solving Linear Systems

Key Learning Outcomes

• Define and recognize functions and their graphs

• Analyze and graph polynomial and rational functions

• Solve equations and inequalities involving linear, quadratic, polynomial, rational, exponential, and logarithmic functions

• Apply properties of logarithms and exponents

• Perform matrix operations and solve linear systems using matrices

Definitions and Examples

Functions and Graphs

• Function: A relation in which each input has exactly one output. Notation: $f(x)$.

• Domain: The set of all possible input values.

• Range: The set of all possible output values.

• Linear Function: $f(x) = mx + b$

• Quadratic Function: $f(x) = ax^2 + bx + c$

• Example: The function $f(x) = 2x + 3$ has domain $(- , 1e)$ and range $(-1e, 1e)$.

Polynomial and Rational Functions

• Polynomial Function: $f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_0$

• Rational Function: $f(x) = \frac{P(x)}{Q(x)}$, where $Q(x) \neq 0$

• Remainder Theorem: If $f(x)$ is divided by $(x - c)$, the remainder is $f(c)$.

• Factor Theorem: $(x - c)$ is a factor of $f(x)$ if and only if $f(c) = 0$.

• Example: $f(x) = x^2 - 4$ can be factored as $(x - 2)(x + 2)$.

Exponential and Logarithmic Functions

• Exponential Function: $f(x) = a^x$, $a > 0$, $a \neq 1$

• Logarithmic Function: $f(x) = \log_a(x)$

• Properties of Logarithms:

  • $\log_a(xy) = \log_a(x) + \log_a(y)$

  • $\log_a(\frac{x}{y}) = \log_a(x) - \log_a(y)$

  • $\log_a(x^r) = r\log_a(x)$

• Example: $\log_{10}(100) = 2$ because $10^2 = 100$.

Matrices and Linear Systems

• Matrix: A rectangular array of numbers arranged in rows and columns.

• Gaussian Elimination: A method for solving systems of linear equations by transforming the system's augmented matrix to row-echelon form.

• Determinant: A scalar value that can be computed from the elements of a square matrix and encodes certain properties of the matrix.

• Inverse Matrix: For a square matrix $A$, the inverse $A^{-1}$ satisfies $AA^{-1} = I$.

• Cramer's Rule: A method for solving a system of linear equations using determinants.

• Example: For the system $\begin{cases} x + y = 2 \\ x - y = 0 \end{cases}$, the solution is $x = 1$, $y = 1$.

Student Responsibilities and Policies

• Attendance is required; students must withdraw officially if they stop attending.

• Online homework and tests are completed via MyMathLab; some tests require proctoring.

• Students must use approved calculators and follow all testing protocols.

• Accommodations are available for students with disabilities.

Additional Resources

• Math Tutoring Lab available for extra help.

• Emergency notifications via Leopard Alert system.

• Mental health counseling and disability accommodations available.