Functions and Graphs Overview

This set of flashcards covers key concepts related to functions and their properties as discussed in the lecture notes.

Domain

The set of all x values at which a function is defined.

Range

The set of all possible values that a function can take.

Linear Function

A function defined by the formula f(x) = mx + n, which graphs as a straight line.

Slope (m)

The ratio of the change in y to the change in x, represented by (y1 - y0)/(x1 - x0).

Y-Intercept (n)

The point where the graph of a function intersects the y-axis.

Implicit Function

A function defined by an equation that must be solved rather than by an explicit formula.

Explicit Function

A function defined by a formula or expression that clearly shows how to compute its output.

Vertical Line Test

A method for determining if a relation is a function; if a vertical line intersects the graph more than once, it is not a function.

Horizontal Line Test

A method for determining if a function is one-to-one; if a horizontal line intersects the graph more than once, it is not one-to-one.

Biggest Possible Domain

The largest set of x values for which a function is well-defined, encompassing all x making the function meaningful.