Chapter 1.3 - The graph of a function

Constant

A function f is constant on an interval when, for any x1 and x2 in the interval f(x1) = f(x2)

Decreasing

A function f is decreasing on an interval when, for any x1 and x2 in the interval x1 < x2 implies f(x1) > f(x2)

Increasing

A function f is increasing on an interval when, for any x1 and x2 in the interval x1 < x2 implies f(x1) < f(x2)

Relative maximum

A function value f(a) is called a relative maximum of f when there exists an interval (x1, x2) that contains a such that x1 < x < x2 implies f(a) => f(x).

Relative minimum

A function value f(a) is called a relative minimum of f when there exists an interval (x1, x2) that contains a such that x1 < x < x2 implies f(a) <= f(x).

Vertical line tests

A set of points in a coordinate plane is the graph of y as a function of x if and only if no vertical line intersects the graph at more than one point.

The graph of a function

The graph of a function f is the collection of ordered pairs (x, f(x)), such that x is in the domain of f.