Which graph represents the piecewise-defined
(see attachment for question)
any is appreciated!

Explanation:

The first thing to notice is that we have an "or equal to" as the first inequality sign in the top row. This means we will have a closed circle at the endpoint here. Because x = 0 is the furthest leftmost x value, this means there is a closed circle when x = 0. So we could stop right here and immediately see the answer is choice D since no other answer choice fits the description.

However, let's keep going. The idea is to graph y = -x+4 only on the interval 0 <= x < 3. So basically we graph for x values between 0 and 3; including 0 but excluding 3. Following these steps will produce the diagonal line you see in graph D. The open circle or hole indicates that the point is not part of the graph. The open circle is from the fact that there is no "or equal to" as part of the right endpoint of the compound inequality 0 <= x < 3. In other words, if we had just x < 3 then we would have an open circle only.

The second piece, the flat piece, is the result of graphing y = 6 when x >= 3. So we graph a horizontal line through y = 6 but only for x values of 3 or larger. Graph D has this feature. The closed circle at the endpoint is because of the "or equal to" portion.

So in summary, you basically graph y = -x+4 and y = 6 as you normally would. However, you erase the portions in which that dont fit the restricted intervals mentioned. Or put another way, you only graph these functions based on what the inequality says.

d

Step-by-step explanation: idk

step-by-step explanation: