Question

what is the domain of this function?

the graph is a coordinate plane with several green points plotted. the x-axis ranges from -5 to 5, and the y-axis ranges from -5 to 5. the points are at (-5, -1), (-2, 2), (-1, 1), (2, 1), (3, -2), and (5, 2).

options:
{ -5, -2, -1, 1, 3, 5 }
{ -2, -1, 1, 2, 5 }
{ -5, -2, -1, 2, 3, 5 }
{ -2, -1, 1, 2 }

Explanation:

Step1: Recall the definition of domain

The domain of a function is the set of all x - values (input values) for which the function is defined. For a discrete function represented by points on a coordinate plane, the domain is the set of x - coordinates of all the points.

Step2: Identify the x - coordinates of the points

Looking at the graph, we identify the x - coordinates of each green dot:

• The first dot has an x - coordinate of - 5.
• The second dot has an x - coordinate of - 2.
• The third dot has an x - coordinate of - 1.
• The fourth dot has an x - coordinate of 2.
• The fifth dot has an x - coordinate of 3.
• The sixth dot has an x - coordinate of 5.

So the domain is the set of these x - coordinates: \(\{-5, - 2, - 1, 2, 3, 5\}\)

Answer:

\(\{-5, - 2, - 1, 2, 3, 5\}\) (the third option)