Final answer:
Both a sequence t(n) and a function f(x) can describe relationships, with a sequence being a function with a domain restricted to integers. f(x)=2·1.3^x is a function with a continuous real number domain, while t(n)=2·1.3^n is a function with a domain of just the integers.
Step-by-step explanation:
Both a sequence and a function describe relationships between numbers, but they do differ in some key ways. A function is a generalized relationship in which each input (often represented by the variable x) is paired with exactly one output. The function f(x) = 2 · 3x is indeed a function as it satisfies this definition — for any real number input x, there's one specific output.
On the other hand, a sequence, such as t(n) = 2 · 3n, is a type of function with the domain specifically restricted to the integers, or a subset of the integers, such as the natural numbers. So, it is still a function, but with a more limited domain. When n is an integer, t(n) is saying that for each integer n, there's a corresponding term in the sequence.
With t(n) being a function with a specific domain (the integers), it usually represents a discrete relationship, while f(x) represents a continuous relationship over all real numbers. For instance, when graphed, f(x) would be a continuous curve, while t(n) would be plotted as individual points at each integer value of n. Both f(x) and t(n) exhibit exponential growth, but f(x) does this for every real number, and t(n) only for integers.