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Linear functions are among the simplest types of functions you will encounter in mathematics. They form a straight line when graphed and have the general form \( y = mx + c \), where \( m \) is the slope of the line and \( c \) is the y-intercept.
In our given function \( y = 125 - 12x \), it can be rewritten in the form \( y = -12x + 125 \). Here, the slope \( m \) is \(-12\), indicating the line tilts downward to the right, and the y-intercept \( c \) is \(125\), which is where the line crosses the y-axis.
Linear functions are lovely because their domain and range are easy to determine. There are no fancy operations like division by zero or square roots of negative numbers to worry about. This simplicity makes linear functions a cornerstone wherever functions are studied.

The concepts of domain and range rely heavily on the set of real numbers, which includes all numbers that can be found on the number line. This includes every integer, fraction, and decimal that you can think of, going off infinitely in both positive and negative directions.

When we talk about the domain of a linear function like \( y = 125 - 12x \), which can be interpreted as basically being defined for all real numbers, we are saying there are no restrictions on \( x \) values. Thus, the domain is \( (-\infty, + \infty) \).
Similarly, for the range, we acknowledge that since \( y \) can also attain any value in real numbers, the range is also \( (-\infty, +\infty) \).

Understanding real numbers and their infinite nature is crucial because it enables us to grasp domains and ranges of linear functions confidently, knowing they extend infinitely without limits.

Input values, often referred to as \( x \)-values, are crucial because they determine the output values in functions. In the function \( y = 125 - 12x \), the input values are the values for \( x \) that we can plug into the function.
For linear functions, input values run across all real numbers, meaning there's no restriction. You can plug in any real number for \( x \), and the function will "happily" return a corresponding \( y \). This lack of restriction is what gives the domain of \( y = 125 - 12x \) its wide-reaching span from \(-\infty\) to \(+\infty\).

When you understand the role of input values, you're better equipped to predict what a function will do -- or at least the type of output values it will produce -- based solely on what values are given to \( x \). For linear functions, there's often nothing off the table as an input.