Final answer:
The range of the function f(x) = -2x + 3 is (-∞, 3], as it decreases without bound but cannot exceed 3.
Step-by-step explanation:
The range of the function f(x) = -2x + 3 can be determined by examining the behavior of the function as x takes on values from negative to positive infinity. Since the coefficient of x is negative (-2), the function is a straight line that slopes downwards as x increases. As such, there is no upper bound to the function's values because as x goes to negative infinity, f(x) will increase without limit. However, as x goes to positive infinity, f(x) will decrease towards negative infinity, so the function does not have a lower bound either.
Therefore, the range of f(x) is all real numbers less than or equal to 3, represented as (-∞, 3].