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In mathematics, a function is a fundamental concept that pairs each input with exactly one output. It's like a machine where you put in a number, and get out another prescribed number.

For example, if we have a function defined by the rule that relates every given input, represented by the variable x, to exactly one output y, then that rule is a function. Mathematically, we might see functions written as something like f(x) = x + 2, which means that if you put in a 3, the output would be 5, because 3 + 2 equals 5.

To determine if a relationship between two variables is a function, we look for each input having one and only one output. This is the 'vertical line test' where if you can draw a vertical line through the graph of the relationship and it touches the graph at only one point, then it is a function. This concept is crucial as it sets the stage for understanding more complex relationships in algebra and calculus.

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. It's essentially a language of its own that allows us to formulate equations that express relationships between quantities.

In algebra, you will often see letters used to represent numbers in equations and functions. These letters are called variables, and they stand in for unknown values that we aim to solve for. Algebra can range from very simple operations, like solving for x in the equation x + 2 = 5, to complex ones involving multiple variables and higher degree equations.

Equations in algebra are ways of representing functions, and as in the exercise example, they can be used to determine if a variable depends on another in a functional way. This means that if we change the value of one variable, it affects the value of the other according to the rule defined by the equation.

A constant function is a special type of function in mathematics where the output value is the same no matter what the input value is. This means that no matter what x value you plug into the equation, the y value will remain the same.

In the context of the given exercise, the equation y = -75 is a perfect example of a constant function. This is because the y value is always -75, regardless of any x value. It's like saying no matter what you do, the outcome will always be the same.

Constant functions have horizontal lines as their graphs since they do not change as x changes. It is important to recognize these types of functions as they often serve as baselines or starting points for more complex functions and can represent fixed relationships in real-life scenarios.