f(x) = (x - 3)2, with domain [3, ∞)

What is the range of function f?

To find the range of a function, we need to determine the set of all possible values that the function can output. In this case, the function is f(x) = (x - 3)^2, with a domain of [3, ∞).

Let's analyze the function step by step:

1. First, note that the only factor affecting the output of the function is the term (x - 3)^2. The square of any value is always non-negative because multiplying any number by itself will result in a positive value (or zero if the number is 0).

2. The term (x - 3) represents the deviation of x from the value 3. Since the domain of the function is [3, ∞), x can only take a value greater than or equal to 3.

3. By squaring the deviation (x - 3), we ensure that the output value is always non-negative.

4. The value of x - 3 can be 0 when x equals 3. In this case, (x - 3)^2 will be 0, which is the minimum possible value of the function.

5. As x increases from 3 onward, the value of (x - 3)^2 will also increase, resulting in an increasing sequence of non-negative values.

Based on this analysis, we can conclude that the range of function f(x) = (x - 3)^2, with domain [3, ∞), is [0, ∞). The function will output all non-negative values, starting from 0 and increasing indefinitely.