A graph of a piecewise defined function is shown on the coordinate plane.A graph of a piecewise defined function is shown on the coordinate plane. The x axis goes from negative 5 to 10 and the y axis goes from negative 10 to 5. The function starts with an arrow pointing down to the left and a line goes up to the right to the point left-parenthesis negative 2 comma negative 2 right-parenthesis. The function then moves horizontally to the right to the point left-parenthesis 2 comma negative 2 right-parenthesis. From here, the function travels up to the right to the point left-parenthesis 4 comma 0 right-parenthesis. The last piece of the function starts here and curves down and to the right passing through the point left-parenthesis 8 comma negative 2 right-parenthesis and ends with an arrow pointing down and to the right.

Question

A graph of a piecewise defined function is shown on the coordinate plane.A graph of a piecewise defined function is shown on the coordinate plane. The x axis goes from negative 5 to 10 and the y axis goes from negative 10 to 5. The function starts with an arrow pointing down to the left and a line goes up to the right to the  point left-parenthesis negative 2 comma negative 2 right-parenthesis. The function then moves horizontally to the right to the point left-parenthesis 2 comma negative 2 right-parenthesis. From here, the function travels up to the right  to the point left-parenthesis 4 comma 0 right-parenthesis. The last piece of the function starts here and curves down and to the right passing through the point left-parenthesis 8 comma negative 2 right-parenthesis and ends with an arrow pointing down and to the right.
Question
Use the graph to answer the question.
Determine the interval on which this function is constant.
(1 point)
Responses

left-parenthesis 4 comma infinity right-parenthesis
Image with alt text: left-parenthesis 4 comma infinity right-parenthesis

left-parenthesis negative infinity comma 4 right-parenthesis
Image with alt text: left-parenthesis negative infinity comma 4 right-parenthesis

left-parenthesis negative 2 comma 2 right-parenthesis
Image with alt text: left-parenthesis negative 2 comma 2 right-parenthesis

left-parenthesis negative infinity comma negative 2 right-parenthesis union left-parenthesis 2 comma 4 right-parenthesis
Image with alt text: left-parenthesis negative infinity comma negative 2 right-parenthesis union left-parenthesis 2 comma 4 right-parenthesis

GPT-4o mini · Answer

The function is constant in the interval where the graph is horizontal. From your description, the function is constant between the points \((-2, -2)\) and \((2, -2)\), where it moves horizontally.

Thus, the interval on which the function is constant is:

\[ \text{left-parenthesis } -2, 2 \text{ right-parenthesis \]

None of the provided response options exactly match the interval \((-2, 2)\). However, if you are looking for intervals in which the function is not changing (constant), that is the correct interval. Please note that it does not exactly align with any of the responses you've listed, as the ranges provided do not include \((-2, 2)\).

Please verify the options once more or provide further context as it might help clarify the situation.