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A graph on a coordinate plane shows a function with two line segments that are disjoint.The coordinate plane has an x-axis range of negative 10 to 10 and a y-axis range of negative 10 to 10. There is a line segment connecting an open point at left-parenthesis negative 7 comma negative 4 right-parenthesis and a closed point at left-parenthesis negative 3 comma 3 right-parenthesis. A second line segment connects an open point at left-parenthesis negative 1 comma 3 right-parenthesis and a closed point at left-parenthesis 2 comma 8 right-parenthesis.

Question
Use the graph of the function to answer the question.
Write the range of the function given in the graph in interval notation.
(1 point)
Responses

left bracket negative 4 comma 8 right bracket
Image with alt text: left bracket negative 4 comma 8 right bracket

left parenthesis negative 4 comma 3 right parenthesis union left parenthesis 3 comma 8 right bracket
Image with alt text: left parenthesis negative 4 comma 3 right parenthesis union left parenthesis 3 comma 8 right bracket

left parenthesis negative 4 comma 8 right bracket
Image with alt text: left parenthesis negative 4 comma 8 right bracket

left bracket negative 4 comma 3 right parenthesis union left parenthesis 3 comma 8 right parenthesis

1 answer

To determine the range of the function represented by the given line segments, we need to analyze the y-values provided by the endpoints of the segments:

  1. The first line segment connects an open point at (-7, -4) and a closed point at (-3, 3):

    • The y-values covered by this segment range from just above -4 (due to the open point) to 3 (since the closed point at (-3, 3) includes this value).

  2. The second line segment connects an open point at (-1, 3) and a closed point at (2, 8):

    • The y-values covered by this segment range from just above 3 (due to the open point) to 8 (since the closed point at (2, 8) includes this value).

Putting this together, we can identify the following ranges:

  • The first segment contributes the range (-4, 3].
  • The second segment contributes the range (3, 8].

Therefore, the complete range of the function can be expressed as: (-4, 3] ∪ (3, 8].

Now, writing this in interval notation, the answer is:

left parenthesis negative 4 comma 3 right bracket union left parenthesis 3 comma 8 right bracket