Chapter 4 Linear Functions

decreasing function

Another way of saying that a graph is going up is that its slope is positive. If the graph is going down, then the slope will be negative. Since slope and derivative are synonymous, we can relate increasing and decreasing with the derivative of a function. First a formal definition.

interval of increase

If f′(x) > 0, then f is increasing on the interval, and if f′(x) < 0, then f is decreasing on the interval. This and other information may be used to show a reasonably accurate sketch of the graph of the function. Example 1: For f(x) = x 4 − 8 x 2 determine all intervals where f is increasing or decreasing.

constant interval

In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants. If it is not a constant it is called a variable. See: Variable. Algebra - Definitions.

increasing function

In fact lines are either increasing, decreasing, or constant. The equation of a line is: y = mx + b. The slope m tells us if the function is increasing, decreasing or constant: m < 0.

constant function

In mathematics, a constant function is a function whose (output) value is the same for every input value. For example, the function is a constant function because the value of is 4 regardless of the input value (see image).

piecewise function

In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function which is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain (a sub-domain).

interval of decrease

Intervals of increase and decrease are the domain of a function where its value is getting larger or smaller, respectively. For a function f(x) over an interval where , f(x) is increasing if and f(x) is decreasing if . For f(x) over a given interval, if f(x) is increasing and if f(x) is decreasing.