Final answer:
The range of the function f(x)={(2x+2,x-3)} is all real numbers.
Step-by-step explanation:
The range of a function represents the set of all possible y-values that the function can output. To find the range of the function f(x) = (2x + 2, x - 3), we need to determine the possible values for the second coordinate. Since there are no restrictions on the value of x, we can say that any real number can be input into the function. So, the range of the function f(x) is the set of all possible values of (x - 3).
In interval notation, the range is represented as (-∞, ∞), meaning that the range extends indefinitely in both the positive and negative directions. In set notation, the range is represented by {y: y ∈ ℝ}, which means all real numbers.
Therefore, the values within the range of f(x)={(2x+2,x-3)} are all real numbers.
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