Final answer:
The linear function f(x) = -2x + 3 does not have a vertex like a parabola, but its y-intercept could be considered as (0, 3). The domain and range of this linear function are both all real numbers.
Step-by-step explanation:
For the given function f(x) = -2x + 3, the vertex form of a quadratic function is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. Since the given function is linear and not quadratic, it does not have a vertex in the same sense that a parabola does. However, if we assume 'vertex' refers to the point where the function intercepts the y-axis, then the vertex would be (0, 3) because that's where the function would intersect the y-axis when x=0.
The domain of any linear function without restrictions is all real numbers, and since this function has a constant negative slope, it continues to decrease as x increases; therefore, the range is also all real numbers. Hence, the correct answer for the vertex should be (0, 3), but since this is not an option, and assuming a typo in the question, the closest matching answer is (3, -1), as it implies a y-intercept at -1, but the x-coordinate should be noted as incorrect. The domain is all real numbers, and the range is also all real numbers, not limited to y <= -1 as suggested by some options.