A graph is shown on the coordinate plane.The function starts at open point left-parenthesis negative 5 comma negative 2 right-parenthesis and is connected by a line segment to closed point left-parenthesis negative 1 comma 2 right-parenthesis which is connected by a line segment to open point left-parenthesis 3 comma 2 right-parenthesis which is connected by a line segment to closed point left-parenthesis 6 comma 5 right-parenthesis.

Question

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

left-parenthesis negative 5 comma 3 right-parenthesis union left-parenthesis 3 comma 6 right-bracket
Image with alt text: left-parenthesis negative 5 comma 3 right-parenthesis union left-parenthesis 3 comma 6 right-bracket

left-parenthesis negative 5 comma 6 right-bracket
Image with alt text: left-parenthesis negative 5 comma 6 right-bracket

left-bracket negative 5 comma negative 1 right-parenthesis union left-parenthesis 1 comma 6 right-parenthesis
Image with alt text: left-bracket negative 5 comma negative 1 right-parenthesis union left-parenthesis 1 comma 6 right-parenthesis

left-parenthesis negative 5 comma negative 1 right-parenthesis union left-parenthesis negative 1 comma 3 right-parenthesis union left-parenthesis 3 comma 6 right-parenthesis

Answer 1

To determine the domain of the function represented by the given points and connections, we should analyze the intervals that the function covers based on the provided open and closed points.

1. Points and Their Types:

   • The graph starts at the open point \((-5, -2)\), which means \(-5\) is not included in the domain.
   • It connects to the closed point \((-1, 2)\), meaning \(-1\) is included in the domain.
   • Then it continues to the open point \((3, 2)\), indicating that \(3\) is not included in the domain.
   • Finally, it connects to the closed point \((6, 5)\), meaning \(6\) is included in the domain.

2. Intervals:

   • The first interval starts just after \(-5\) (so it is \((-5, -1]\)).
   • The second interval starts just after \(-1\) and goes up to just before \(3\) (so it is \((-1, 3)\)).
   • The last interval spans from \(3\) to \(6\) inclusive (so it is \((3, 6]\)).

Putting this all together, the total domain can be expressed in interval notation as: \[ (-5, -1] \cup (-1, 3) \cup (3, 6] \]

So the correct response from the options provided is: left-parenthesis negative 5 comma negative 1 right-parenthesis union left-parenthesis negative 1 comma 3 right-parenthesis union left-parenthesis 3 comma 6 right-parenthesis.