Pre-Calculus BC Honors Lecture Notes 2025-2026

These flashcards cover key concepts in Pre-Calculus BC, focusing on vocabulary terms essential for understanding the material.

Function

A relation where each input value results in exactly one output value.

Domain

The set of all input values that produce an output value.

Range

The set of all possible outputs of a function.

Vertical Line Test

If a vertical line intersects a graph at more than one point, it is not a function.

Factorial

An expression denoted by n! defined as the product of all positive integers up to n.

Graph transformations

Changes made to the graph of a function, including shifts, stretches, and reflections.

Continuous function

A function is considered continuous at a point if the graph can be drawn without lifting the pencil.

Even function

A function where f(x) = f(-x) for all x in the domain; it is symmetric about the y-axis.

Odd function

A function where f(-x) = -f(x) for all x in the domain; it is symmetric about the origin.

Interval notation

A shorthand way to express intervals using starting and ending values, with parentheses for open endpoints and brackets for closed endpoints.

Asymptote

A line that a graph approaches but never touches or crosses.

Inverse function

A function that reverses the effect of the original function; if f(x) = y, then f⁻¹(y) = x.

Cosecant

The reciprocal function for sine; csc(x) = 1/sin(x).

Secant

The reciprocal function for cosine; sec(x) = 1/cos(x).

Polynomial

A sum of one or more power functions of non-negative integer exponents.

Power function

A function of the form f(x) = a * x^p, where a and p are constants.

Sigma notation

A notation used to represent the sum of a sequence of terms.

Factorization

Re-writing an expression as a product of its factors.

NaturalLOg

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.71828. It is the inverse function of the exponential function e^x.