A graph of the sequence f(n)=2n-3 and a graph of the function f(x)=2x-3 are both shown
What accounts for the differences between the graphs in terms of range?
i know only the difference of the domain but i have no idea the difference of the range can someone please help
To understand the difference in the range between the graphs of the sequence and the function, let's first clarify the concepts of sequence and function:
1. Sequence: A sequence is an ordered list of numbers. In this case, the sequence f(n) = 2n - 3 represents a list of values obtained by plugging natural numbers (n = 1, 2, 3, ...) into the expression 2n - 3.
2. Function: A function relates each input value (x) to a unique output value (f(x)). In this case, the function f(x) = 2x - 3 represents a mathematical relationship between an input value (x) and the corresponding output value (f(x)) obtained by applying the expression 2x - 3.
Now, let's consider the difference in the range between the sequence and the function:
1. Sequence range: The range of a sequence represents the set of all possible output values (terms) in the sequence. In this case, the sequence f(n) = 2n - 3 produces a range of numbers that can be obtained by substituting natural numbers into the expression. For example, if we plug n = 1, we get f(1) = 2(1) - 3 = -1. As we continue plugging in larger natural numbers, the range of the sequence increases.
2. Function range: The range of a function represents the set of all possible output values obtained by applying the function to different input values. In this case, the function f(x) = 2x - 3 represents a continuous mathematical relationship. By plugging in any real number into the expression, we can obtain a corresponding output value. For example, if we plug x = 1, we get f(1) = 2(1) - 3 = -1. Similarly, if we plug x = 2, we get f(2) = 2(2) - 3 = 1. The range of the function includes all possible values obtained by plugging in any real number.
In summary, the key difference between the range of the sequence and the range of the function lies in the nature of the input values. While the sequence uses natural numbers as inputs, the function allows for any real number input, resulting in a broader and continuous range.