Algebra 2
There is a graphs of the sequence f(n)=2n-3 and a graph of the function f(x)=2x-3
What difference exist between the two graphs?
What accounts for the differences between the graphs in terms of domain and range?
Help please I don't understand
f(n) is a sequence of integers, and the domain is all integers.
f(x) is a function whose domain is all real numbers, not just integers.
The given sequence and function both have the same formula: f(n) = 2n - 3 and f(x) = 2x - 3. The difference lies in the interpretation of the input variable.
In the sequence, the variable n typically represents the position or index of a term in a list or sequence. Substituting different values for n will give you the corresponding terms of the sequence. The graph of the sequence will consist of separate points, plotted as (n, f(n)).
In the function, the variable x typically represents a value on the x-axis of a coordinate plane. Substituting different values for x will give you the corresponding values of the function. The graph of the function will typically be a continuous line.
Now, let's consider the differences in terms of domain and range:
Domain:
For the sequence f(n) = 2n - 3, the domain consists of all possible values for n. When dealing with sequences, n is often limited to positive integers, starting from 1 or 0, depending on the context. For example, you can have terms like f(1), f(2), f(3), etc.
For the function f(x) = 2x - 3, the domain can include any real numbers. You can substitute any value of x, positive or negative, whole numbers or fractions, into the function.
Range:
For both the sequence and the function, the range refers to the set of values that f(n) or f(x) can take. In this case, the range is simply all real numbers because for any given n or x, f(n) or f(x) will always produce a real number.
To summarize, the main differences between the two graphs lie in their interpretation of the input variable (n vs. x) and their representation (sequence vs. function). The domain for the sequence is typically limited to positive integers, while the domain for the function can include any real number. However, the range for both the sequence and the function is all real numbers.