Question

give the domain and the range of the function whose graph is shown to the right. when arrows are drawn, assume the function continues in the indicated direction. the domain is \\(\square\\). (type your answer in interval notation.)

Explanation:

Step1: Determine the domain from the graph

The domain of a function is the set of all x - values for which the function is defined. Looking at the graph, we can see that the left - most point of the graph (in terms of x - values) seems to be at \(x=-6\) (since the graph starts to the left around \(x = - 6\)) and the right - most point (where the arrow is going) extends to the right, but wait, actually, looking at the x - axis, the graph's left end is at \(x=-6\) and the right end (the arrow at the bottom) is at \(x = 8\)? Wait, no, let's re - examine. Wait, the graph: the lower part has an arrow at \(x = 8\) (on the x - axis, the x - coordinate of the arrow is 8? Wait, no, the x - axis is horizontal. Let's look at the x - values. The graph spans from \(x=-6\) (the left - most point of the curve) to \(x = 8\) (the right - most point of the curve)? Wait, no, actually, when we look at the graph, the left - most x - value where the graph exists is \(x=-6\) and the right - most x - value is \(x = 8\)? Wait, no, let's check the x - axis. The x - axis has markings. Wait, the graph: the left part of the curve starts at \(x=-6\) (the left - most point) and the right part (the lower curve) ends at \(x = 8\) (the x - coordinate of the arrow is 8). Wait, actually, the domain is the set of all x - values from the left - most to the right - most points of the graph. So the left - most x is \(-6\) and the right - most x is \(8\)? Wait, no, looking at the graph again, the left - most point (the start of the upper curve) is at \(x=-6\) (the y - value is around 0? Wait, no, the grid: each square is 1 unit. Let's see, the upper curve starts at \(x=-6\) (x - coordinate) and goes to the right, and the lower curve starts from the left (around \(x=-6\)) and goes to \(x = 8\) (the x - coordinate of the arrow at the bottom). Wait, actually, the domain is all real numbers from \(-6\) to \(8\)? Wait, no, the graph: the left - most x - value is \(-6\) (inclusive) and the right - most x - value is \(8\) (inclusive)? Wait, no, let's check the x - axis. The x - axis has labels from - 10 to 10. The graph's left end (the upper curve) is at \(x=-6\) (x - coordinate) and the right end (the lower curve) is at \(x = 8\) (x - coordinate). So the domain is the interval of x - values from \(-6\) to \(8\), including both endpoints? Wait, no, wait the graph: the upper curve starts at \(x=-6\) (x=-6, y = 0? Wait, no, the upper curve: when x=-6, y = 0? Then it goes up, and the lower curve: when x = 8, y=-8? Wait, no, the arrow at the bottom is at \(x = 8\), \(y=-8\). Wait, actually, the domain is the set of all x - values for which the function is defined. So from the left - most x (\(-6\)) to the right - most x (\(8\)). So the domain in interval notation is \([-6,8]\)? Wait, no, wait, maybe I made a mistake. Wait, the graph: the left - most point (the start of the upper curve) is at \(x=-6\) (x - coordinate) and the right - most point (the end of the lower curve) is at \(x = 8\) (x - coordinate). So the domain is \([-6,8]\). Wait, but let's confirm. The domain is all x such that the graph exists. So the left - most x is \(-6\) and the right - most x is \(8\), so the domain is \([-6,8]\).

Step2: Write the domain in interval notation

Interval notation for a closed interval (including the endpoints) is \([a,b]\) where \(a\) is the left - most value and \(b\) is the right - most value. Here, \(a=-6\) and \(b = 8\), so the domain is \([-6,8]\).

Answer:

\([-6, 8]\)