What (Positive Linear Function Machine)

What is the Positive Linear Function Machine Activity?

College Algebra Related Pages: 180-181 "Functions"
Trigonometry Related Pages: 7 "Functions"
College Algebra and Trigonometry Related Pages: 180-181 "Functions"
Precalculus Related Pages: 98-99 "Functions"

This activity allows the user to explore linear functions.

The function is determined by looking for patterns in the outputs. The functions available for exploration in the function machine activity have one of the following forms:

f(x) = mx + b

where m and b can be any integers between 0 and 10.

The notion of a function is important in higher mathematics such as calculus and in areas which use mathematics such as physics. Any rule that assigns exactly one output to one or more inputs can be called a function.

Here are a few examples:

Input the number of seconds after the starting gun in a race to get an output of the number of meters the runner has covered.

input 3 2 0 -4

output 4 -1 2 -3
f(x) = x - 6, where x is the independent variable for the input and f(x) is the dependent variable for the output.

The rule about only one output to an input is crucial to the definition of a function. For example, the table below, although it is a relation, cannot represent a function because the input 3 has two different outputs:

input	3	2	0	3
output
4
-1
2
-3

Note that in this applet the variable y is used instead of the notation f(x).

The functions produced by this machine are special because they all graph as straight lines. In fact, the slope of the line and the y-intercept of the line are easy to read from the formula:

y = (slope) * x + (y-intercept)

The slope, designated as m, tells us the rise over the run. The y-intercept, designated by b, tells us where the line crosses the vertical axis when plotted:

Here the red line has intercept = 7 and slope = -1/2, and the green line has intercept = -1 and slope = 4/2 = 2/1.