Final answer:
The given sequence -3, -7, -11, -15 is a function because each position in the sequence has exactly one associated value. The function has the form f(n) = -4n + 1, which indicates a negative slope.
Step-by-step explanation:
The sequence given is -3, -7, -11, -15, and so on. A function, in mathematical terms, is a relation in which each input (often named 'x') is assigned to exactly one output (often named 'f(x)' or 'y').
Let's look at the sequence as a set of ordered pairs where the first term of each pair corresponds to the position in the sequence (1, 2, 3, ...) and the second term is the value of the sequence at that position (-3, -7, -11, ...). We can represent this as (1, -3), (2, -7), (3, -11), (4, -15), and so on. In this context, the 'input' is the position number, and the 'output' is the value of the sequence at that position. Since each position (input) leads to exactly one value (output), this sequence is indeed a function.
The rule that generates the sequence is f(n) = -4n + 1, where 'n' is the position in the sequence. This function has a negative slope, as visualized by the decreasing numbers in the sequence.