A graph is shown on the coordinate plane.The x-axis goes from negative 6 to 6 and the y-axis goes from negative 2 to 10. The function starts at closed point left-parenthesis negative 3 comma 0 right-parenthesis and is connected by a line segment to closed point left-parenthesis 0 comma 3 right-parenthesis which is connected by a line segment to closed point left-parenthesis 2 comma 7 right-parenthesis which is connected by a line segment to open point left-parenthesis 5 comma 8 right-parenthesis.

Question

Question
Use the graph of the function to answer the question.
Identify the range of the graphed function.
(1 point)
Responses

left brace y vertical bar 0 less than y less than or equals 8 right brace
Image with alt text: left brace y vertical bar 0 less than y less than or equals 8 right brace

left brace y vertical bar 0 less than or equals y less than 8 right brace
Image with alt text: left brace y vertical bar 0 less than or equals y less than 8 right brace

left brace y vertical bar negative 3 less than or equals y less than or equals 5 right brace
Image with alt text: left brace y vertical bar negative 3 less than or equals y less than or equals 5 right brace

left brace y vertical bar negative 3 less than or equals y less than 5 right brace
Image with alt text: left brace y vertical bar negative 3 less than or equals y less than 5 right brace

Answer 1

To determine the range of the graphed function, we need to look at the y-values that are covered by the line segments described.

1. The function starts at the closed point \((-3, 0)\), so the lowest value of \(y\) is 0 (inclusive), because it's a closed point.
2. The line goes up to the closed point \((0, 3)\), so \(y\) continues up to 3 (inclusive).
3. The next segment goes from \((0, 3)\) to \((2, 7)\), where \(y\) reaches up to 7 (inclusive) at \((2, 7)\).
4. Finally, the function goes to the open point \((5, 8)\). Since this point is open, \(y\) can approach 8, but cannot include it.

Thus, the range of the function is from 0 (including) to just below 8 (not including). Therefore, we can express the range in interval notation as:

\[ { y \mid 0 \leq y < 8 } \]

So, the correct response that fits this description is:

left brace y vertical bar 0 less than or equals y less than 8 right brace