Calculus I Course Overview and Function Fundamentals

Vocabulary flashcards covering introductory course policies, grading metrics, and basic concepts of functions and transformations from Chapter 1 through Chapter 7.

Teaching Assistant (TA)

The primary point of contact for students seeking help with calculus questions, recitation quizzes, or homework problems.

Pearson's MyLab Grace Period

A two-week trial period provided by Pearson allowing students to sign up and access the online textbook and homework assignments before purchasing access.

Dropped Assignment Policy

A course policy stating that the $3$ lowest homework scores and the $3$ lowest quiz scores will be omitted from the final grade calculation.

Exam Format

Common, multiple-choice, machine-graded midterm and final examinations with no partial credit, held in the evening from $8:00\text{ PM}$ to $9:00\text{ PM}$.

Course Grade Weighting

The evaluation structure consisting of 10\text{\null}\null\text{\%} homework, 12\text{\null}\null\text{\%} quizzes, 18\text{\null}\null\text{\%} for each of the three midterms (totaling 54\text{\null}\null\text{\%}), and 24\text{\null}\null\text{\%} for the final exam.

AI Policy

The course rule permitting the use of AI tools to explore and understand material, while requiring all submitted homework to be the student's own work.

Function

A rule $y = f(x)$ that assigns exactly one output $y$ to each permitted input $x$.

Vertical Line Test

A visual method to determine if a graph is a function, requiring that any vertical line intersects the graph at most once.

Domain

The set of all allowed input values ($x$) for a given function.

Range

The set of all possible output values ($y$) produced by a given function.

Function Composition

An operation denoted as $(f \text{ o } g)(x) = f(g(x))$, where the inner function $g(x)$ is evaluated first and its output is passed into the outer function $f(x)$; this operation is generally non-commutative.

Square Root Identity Caution

The algebraic property where \n\sqrt{x^2} = x\n for $x \ge 0$, but \n\sqrt{x^2} = -x\n for $x < 0$ (or overall \n\sqrt{x^2} = |x|\n).

Horizontal Shift Left

A graph transformation represented by $y = f(x + h)$ where $h > 0$, shifting the graph $h$ units to the left.

Vertical Shift Up

A graph transformation represented by $y = f(x) + k$ where $k > 0$, shifting the graph $k$ units upward.

Reflection over the Y-Axis

A graph transformation represented by $y = f(-x)$, which negates the input and flips the graph horizontally across the vertical axis.

Reflection over the X-Axis

A graph transformation represented by $y = -f(x)$, which negates the overall output and flips the graph vertically across the horizontal axis.

Even Function

A function satisfying $f(-x) = f(x)$ for all $x$ in its domain, displaying visual symmetry across the $y$-axis.

Odd Function

A function satisfying $f(-x) = -f(x)$ for all $x$ in its domain, displaying visual rotational symmetry about the origin.