Pre-Calculus I: Elementary Functions

These flashcards cover key concepts related to functions, their compositions, inverses, exponential growth and decay, and logarithms as outlined in the lecture notes.

Composition of Functions

The process of combining two functions such that the output of one function becomes the input of another.

Exponential Function

A mathematical function in the form f(x) = a * b^x where a is a constant and b is the base of the exponent.

Inverse Function

A function that reverses the effect of the original function; denoted as f^(-1)(x).

Continuous Compounding

The process of calculating interest in such a way that it is added continuously, resulting in the formula A = Pe^(rt).

Growth Factor

In exponential growth, the factor by which a quantity increases over a specified time period.

Logarithm

The inverse operation to exponentiation; it determines how many times one number (the base) must be multiplied by itself to obtain another number.

Natural Logarithm

The logarithm to the base e, where e is approximately equal to 2.71828, commonly denoted as ln.

Effective Annual Rate (EAR)

The annual rate of interest that reflects compounding over a year.

Nominal Interest Rate

The stated interest rate on a loan or financial product, not adjusted for inflation or other factors.

Exponential Decay

A decrease in quantity at a rate proportional to its current value, resulting in the formula A = Pe^(-kt).