Question

state the domain and range of the graph in interval notation.
what is the domain? answer in interval notation.
-10,5
not quite.
what is the range? answer in interval notation.

Explanation:

Step1: Determine Domain

The domain is the set of all x - values the graph covers. The leftmost point is at \( x=-10 \) (closed dot, so included) and the rightmost point is at \( x = 5 \) (closed dot, so included). So the domain in interval notation is \([-10,5]\)? Wait, no, wait. Wait, the user's initial answer was marked wrong. Wait, maybe I misread the graph. Wait, let's check again. Wait, the x - axis: the left point is at \( x=-10 \), y = 0 (closed dot), then the graph goes up to a peak, then down to \( x = 5 \), y = 2 (wait, maybe the grid? Wait, the grid lines: each square is 1 unit? Wait, the left dot is at (-10, 0), the peak is at (0, 4) or (0, 5)? Wait, the y - axis has 5 and 10. Wait, the left dot is at (-10, 0) (closed), the right dot is at (5, 2) (closed)? Wait, no, maybe the x - values: the leftmost x is - 10, rightmost x is 5. So domain should be \([-10,5]\). Wait, maybe the user's mistake was in the notation? Wait, interval notation uses square brackets when endpoints are included. So \([-10,5]\) is correct for domain. Wait, maybe the range? Wait, the range is the set of y - values. The lowest y - value is 0 (at x=-10) and the highest y - value is 4 or 5? Wait, the peak is at y = 4? Wait, the grid: from y = 0 (the x - axis) up to y = 4? Wait, no, the graph starts at (-10, 0), goes up to a point at (0, 4) (since from x=-10 to x = 0, it's a line, then from x = 0 to x = 5, it's a line down to (5, 2)? Wait, no, the right dot is at (5, 2)? Wait, maybe I misread the y - coordinate of the right dot. Wait, the right dot is on the horizontal line at y = 2? Wait, no, the x - axis is y = 0, then the next line is y = 2? Wait, no, the grid lines: each vertical and horizontal line is 1 unit. So the left dot is (-10, 0), the peak is at (0, 4) (since from x=-10 to x = 0, it's a line with slope (4 - 0)/(0 - (-10))=4/10 = 2/5, then from x = 0 to x = 5, slope (2 - 4)/(5 - 0)=-2/5, so the right dot is at (5, 2). So the y - values: the minimum y is 0 (at x=-10) and the maximum y is 4 (at x = 0). So the range is \([0,4]\)? Wait, no, maybe the peak is at y = 4? Wait, the y - axis has 5 as a label. Wait, the horizontal line at y = 5 is there. Wait, maybe the peak is at y = 4? No, maybe the peak is at y = 4. Wait, let's re - evaluate.

Wait, the problem is to find domain and range. Let's start with domain:

Step1: Find Domain

The domain is the set of all x - coordinates of the points on the graph. The leftmost point has x=-10 (closed dot, so included) and the rightmost point has x = 5 (closed dot, so included). So domain is \([-10,5]\).

Step2: Find Range

The range is the set of all y - coordinates. The lowest y - value is 0 (at x=-10) and the highest y - value is 4 (at the peak, say x = 0). Wait, no, if the peak is at y = 4, then the range is \([0,4]\). Wait, but maybe the peak is at y = 4. So the range is from 0 to 4, inclusive.

Wait, but the user's initial domain answer was \([-10,5]\) which was marked wrong. Wait, maybe the graph has a different x - range. Wait, maybe the left dot is at (-10, 0) and the right dot is at (5, 2), but maybe the x - values are from - 10 to 5, so domain is \([-10,5]\). Maybe the system made a mistake? Or maybe I misread the graph.

Wait, let's assume the graph is a piece - wise linear function with left endpoint (-10, 0) (closed), right endpoint (5, 2) (closed), and a peak at (0, 4) (closed). Then:

Domain: all x from - 10 to 5, inclusive: \([-10,5]\)

Range: all y from 0 (minimum at (-10, 0)) to 4 (maximum at (0, 4)), inclusive: \([0,4]\)

Wait, but the user's question is about domain. Let's confirm:

Domain: The set of x - values. The graph starts at x=-10 and ends at x = 5, with no breaks, and endpoints included. So domain is \([-10,5]\).

Answer:

Domain: \([-10,5]\), Range: \([0,4]\) (assuming the peak is at y = 4). But wait, maybe the peak is at y = 4. So for domain, the correct interval notation is \([-10,5]\).