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A discrete domain consists of distinct, separate values for the input variable of a function. Unlike a continuous domain, where values can be infinitely small or can take any value in an interval, a discrete domain is composed of specific points.
When dealing with discrete domains, it's crucial to compute the function's value at each point individually.
For the exercise, the discrete domain provided is comprised of the integer values \(x = 0, 1, 2, 3, 4, 5\). There's no need for values in between. This characteristic makes calculations straightforward and allows for an exact representation when we aim to understand the function behavior.

Ordered pairs are a fundamental concept in understanding functions and their graphs. Each ordered pair consists of two elements: an input and a corresponding output.
In mathematics, this is expressed as \( (x, P(x)) \), where \(x\) is the domain value and \(P(x)\) is the function's output at that specific value.
For the given exercise, the function \(P(x) = 3 - 0.6x\) yielded the following ordered pairs based on the discrete domain:

• \((0, 3)\)
• \((1, 2.4)\)
• \((2, 1.8)\)
• \((3, 1.2)\)
• \((4, 0.6)\)
• \((5, 0)\)

These ordered pairs establish a clear relation between each input and its output.

Linear functions are a type of function that create straight lines when graphed on a coordinate plane. Their general form is \(y = mx + b\).
Here, \(m\) represents the slope, which indicates the steepness and direction of the line, and \(b\) represents the y-intercept, which is where the line crosses the y-axis.
For the function \(P(x) = 3 - 0.6x\), we identify a slope of \(-0.6\) and a y-intercept of \(3\). This negative slope shows that as \(x\) increases, \(P(x)\) decreases. Understanding these parameters helps in predicting and plotting the function's path on the graph.

To graph functions, especially those involving linear relationships, we plot ordered pairs on a Cartesian coordinate system. The x-axis (horizontal) represents input values, while the y-axis (vertical) corresponds to output values.
Once we have our ordered pairs—as derived from the function table in the exercise—we place a point at each coordinate on the graph.
Connecting these points results in a visualization of the function's behavior.
For linear functions, such as \(P(x) = 3 - 0.6x\), the graph will show a straight line. Even in a discrete domain, connecting dots gives a sense of how the function behaves between these discrete points, although intermediate values aren't calculated in our specific case.