Study Guide: College Algebra Syllabus and Core Topics Overview

Course Overview: Math 1015 Applied College Algebra

This study guide summarizes the structure, expectations, and core mathematical topics of Math 1015 Applied College Algebra, as outlined in the course syllabus. The course emphasizes foundational algebraic concepts, function analysis, and applications relevant to college-level mathematics.

Course Description and Structure

• Course Focus: Solving equations and inequalities, analyzing function properties and graphs, and working with linear, quadratic, polynomial, exponential, and logarithmic functions.

• Prerequisites: Appropriate placement test score, Math ACT subscore of 19+, or completion of prerequisite courses.

• Textbook: College Algebra in Context, 6th edition by Harshbarger and Yocco (e-text access via MyMathLab).

• Technology: MyMathLab for assignments and lecture videos; graphing calculator (TI-84 or TI-83 recommended; CAS calculators prohibited).

Course Outcomes

• CO1: Solve equations and inequalities algebraically and graphically.

• CO2: Evaluate and interpret function values.

• CO3: Graph functions.

Core Topics and Module Breakdown

Module 1: Functions, Models, and Graphs

This module introduces the foundational concepts of functions and their graphical representations.

• Function and Relation: A function is a relation in which each input (domain value) corresponds to exactly one output (range value).

• Function Notation: Expressed as $f(x)$, where $x$ is the input variable.

• Domain and Range: The domain is the set of all possible input values; the range is the set of all possible output values.

• Graphing Functions: Functions can be graphed by plotting points $(x, f(x))$ and analyzing their behavior visually.

• Example: For $f(x) = 2x + 3$, the domain is all real numbers, and the range is also all real numbers.

Module 2: Linear Functions, Equations, and Inequalities

This module focuses on linear relationships, their algebraic and graphical solutions, and applications.

• Linear Function: A function of the form $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

• Intercepts: The points where the graph crosses the axes. For $y$-intercept, set $x=0$; for $x$-intercept, set $f(x)=0$.

• Slope: The rate of change, calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$.

• Solving Linear Equations: Find $x$ such that $ax + b = 0$.

• Linear Inequalities: Expressions like $ax + b > 0$; solutions are intervals on the real line.

• Example: Solve $2x - 5 = 7$; $x = 6$.

Module 3: Quadratic, Piecewise-Defined, and Power Functions

This module explores quadratic equations, piecewise functions, and power/root functions.

• Quadratic Function: $f(x) = ax^2 + bx + c$, where $a \neq 0$.

• Graph: The graph is a parabola; vertex at $x = -\frac{b}{2a}$.

• Solving Quadratic Equations: Methods include factoring, completing the square, and the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Piecewise Functions: Defined by different expressions over different intervals of the domain.

• Power and Root Functions: Functions of the form $f(x) = x^n$ or $f(x) = \sqrt[n]{x}$.

• Example: $f(x) = \begin{cases} x^2 & x < 0 \\ 2x + 1 & x \geq 0 \end{cases}$

Module 4: Graph Transformations and Algebra of Functions

This module covers how to manipulate and combine functions to create new ones.

• Graph Transformations: Shifting, reflecting, stretching, or compressing the graph of a function.

• Combining Functions: Addition, subtraction, multiplication, division, and composition: $(f \circ g)(x) = f(g(x))$.

• One-to-One Functions: Each output is produced by exactly one input; passes the horizontal line test.

• Inverse Function: If $f(x)$ is one-to-one, its inverse $f^{-1}(x)$ satisfies $f(f^{-1}(x)) = x$.

• Example: If $f(x) = 2x + 3$, then $f^{-1}(x) = \frac{x - 3}{2}$.

Module 5: Exponential and Logarithmic Functions and Equations

This module introduces exponential growth/decay and their inverse, logarithmic functions.

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

• Logarithmic Function: $f(x) = \log_b(x)$, the inverse of the exponential function.

• Properties:

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

  • $\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$

  • $\log_b(x^r) = r \log_b(x)$

• Solving Equations: Use properties of exponents and logarithms to solve for unknowns.

• Example: Solve $2^x = 8$; $x = 3$.

Module 6: Rational Equations

This module focuses on equations involving rational expressions (ratios of polynomials).

• Rational Equation: An equation containing one or more rational expressions, e.g., $\frac{1}{x} + 2 = 3$.

• Solving: Multiply both sides by the least common denominator (LCD) to clear fractions, then solve the resulting equation.

• Check for Extraneous Solutions: Solutions that make any denominator zero must be excluded.

• Example: Solve $\frac{2}{x} = 4$; $x = 0.5$.

Assessment and Grading Structure

Grade Breakdown

Component	Percentage
Homework Assignments (including Moodle assignments)	20%
Tests (4 at 12% each)	48%
Final Exam	32%

Grading Scale

Percentage	Letter Grade
90%–100%	A
80%–89%	B
70%–79%	C
60%–69%	D
0%–59%	F

Assessment Types

• Homework: Assigned via MyMathLab; unlimited attempts before due date; must score at least 70% on test reviews before taking tests.

• Tests: Four topic-based tests, each proctored, covering specific chapters.

• Final Exam: Cumulative, covering all modules.

Course Policies and Support

• Academic Integrity: Strict adherence to LSUE Code of Student Conduct; violations result in disciplinary action.

• Accessibility: Accommodations available through the Office of Disability Services.

• Engagement: Regular participation and timely completion of assignments are required for success.

• Technical Support: Assistance available for Moodle, MyMathLab, and proctoring services.

Summary Table: Module Topics and Associated Chapters

Module	Main Topics	Related Chapters
1	Functions, Models, Graphs	Ch.1
2	Linear Functions, Equations, Inequalities	Ch.2
3	Quadratic, Piecewise, Power Functions	Ch.3
4	Graph Transformations, Algebra of Functions	Ch.4
5	Exponential and Logarithmic Functions	Ch.5
6	Rational Equations	Ch.6

Additional info:

• This syllabus aligns closely with standard College Algebra topics and provides a clear structure for exam preparation.

• Students are encouraged to use the pacing guide and complete all assignments on time to ensure mastery of material.