Question

what is the domain of this relation? (grid with points plotted, and four multiple - choice options for the domain: {-5, -4, 2, 5}, {-5, -4, -1, 2, 5}, {-4, -1, 0, 2, 5}, {-5, -4, -1, 0, 4})

Explanation:

Step1: Identify x - coordinates

Find the x - values (horizontal coordinates) of each plotted point. The points are at \(x=-4\), \(x = - 1\), \(x=2\), \(x = 5\) and \(x=-5\) (wait, let's check the graph again. Wait, the points: one at \(x=-4\) (y around 2 and y around - 4), one at \(x=-1\) (y = 0), one at \(x = 2\) (y=-1), one at \(x = 5\) (y = 4), and also check if there is a point at \(x=-5\)? Wait no, wait the x - coordinates of the points: let's list all the x - values of the plotted points. From the graph, the points have x - coordinates: \(-5\)? Wait no, the first point (left - most) seems to be at \(x=-4\) (two points: one with y = 2, one with y=-4), then \(x=-1\) (y = 0), \(x = 2\) (y=-1), \(x = 5\) (y = 4). Wait, maybe I missed \(x=-5\)? No, the x - axis labels are - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5. Wait, let's list all the x - coordinates of the points:

Looking at the plotted points:

1. Point with x=-4 (two points, but x is - 4)
2. Point with x=-1 (y = 0)
3. Point with x=2 (y=-1)
4. Point with x=5 (y = 4)
5. Wait, is there a point at x=-5? No, the left - most vertical line is x=-5, but the points: let's check the options. The second option is \(\{-5,-4,-1,2,5\}\). Wait, maybe I made a mistake. Wait, the domain is the set of all x - values of the relation. Let's re - examine the graph. The points:

• One point at \(x=-4\) (y = 2)
• One point at \(x=-4\) (y=-4)
• One point at \(x=-1\) (y = 0)
• One point at \(x=2\) (y=-1)
• One point at \(x=5\) (y = 4)
• Wait, is there a point at \(x=-5\)? No, but the option \(\{-5,-4,-1,2,5\}\) includes - 5. Wait, maybe the left - most point has x=-5? Wait, the first vertical line is x=-5, maybe there is a point at x=-5? Wait, no, the plotted points: let's count the x - coordinates. The options:

Option 2: \(\{-5,-4,-1,2,5\}\)

Let's check each x in the option:

• x=-5: Is there a point with x=-5? Maybe I missed it.
• x=-4: Yes, two points.
• x=-1: Yes.
• x=2: Yes.
• x=5: Yes.

The other options:

First option: \(\{-5,-4,2,5\}\) misses - 1.

Third option: \(\{-4,-1,0,2,5\}\) includes 0 (no point at x = 0) and misses - 5.

Fourth option: \(\{-5,-4,-1,0,4\}\) includes 0 and 4 (no point at x = 0 or x = 4) and misses 2,5.

So the correct domain should include x=-5, - 4, - 1, 2, 5.

Step2: Match with options

The set of x - values (domain) is \(\{-5,-4,-1,2,5\}\), which matches the second option.

Answer:

\(\{-5,-4,-1,2,5\}\) (the second option: \(\{-5,-4,-1,2,5\}\))