give the domain and the range of the function whose graph is shown to the right. when arrows are drawn…

Explanation:

Step1: Identify the leftmost and rightmost x - values

Looking at the graph, the leftmost point of the graph (where the curve starts on the left) has an x - value of - 8, and the rightmost point (where the curve ends on the right) has an x - value of 5. Since the graph is a continuous curve (as indicated by the arrows suggesting it continues in the implied direction, but for the domain, we look at the visible part's horizontal extent and the continuation logic), the domain is all real numbers from - 8 to 5, including - 8 and 5? Wait, no, wait. Wait, looking at the graph again: Wait, the left - hand curve has a vertex at x=-8 (since it touches the x - axis at x = - 8? Wait, no, the bottom curve has a vertex at x = 5? Wait, maybe I misread. Wait, the graph: Let's check the x - coordinates. The left - most point of the graph (the left curve) has its left - most x - value? Wait, no, the graph is symmetric? Wait, no, looking at the x - axis (horizontal axis), the left curve (the upper left curve) has a left - most x? Wait, no, the graph's horizontal extent: the left - most x - value where the graph exists is - 8, and the right - most x - value where the graph exists is 5? Wait, no, maybe I made a mistake. Wait, the graph: the left curve (the upper one) has a vertex at x=-8? Wait, no, the bottom curve has a vertex at x = 5? Wait, no, let's look at the grid. The x - axis: the left curve (the one with the arrow pointing left) has its left - most point? Wait, no, the domain is the set of all x - values for which the function is defined. From the graph, the left - most x - value is - 8 (since the curve starts at x=-8, or the left - most point of the graph is at x=-8) and the right - most x - value is 5 (since the right - most point of the graph is at x = 5). Wait, no, maybe the graph is a function where the domain is from - 8 to 5, inclusive? Wait, no, let's re - examine. Wait, the graph: the left curve (upper) has a vertex at x=-8? Wait, no, the bottom curve has a vertex at x = 5? Wait, no, the x - coordinates: the left - most x is - 8, and the right - most x is 5. So the domain is all real numbers from - 8 to 5, including - 8 and 5? Wait, no, maybe the graph is such that the domain is ([-8,5])? Wait, no, maybe I messed up. Wait, let's check the graph again. The left curve (the upper left) has a left - most x - value of - 8 (since it touches the x - axis at x=-8? No, it's a parabola - like shape. Wait, the domain of a function is the set of all x for which y is defined. So from the graph, the horizontal extent: the left - most x is - 8, the right - most x is 5. So the domain is ([-8,5]). Wait, but maybe I made a mistake. Wait, the problem says "when arrows are drawn, assume the function continues in the indicated direction". Wait, the arrows: the upper arrow is pointing left, the lower arrow is pointing right? Wait, no, the upper arrow is pointing left, the lower arrow is pointing right. Wait, maybe the graph is a function that has a domain from - 8 to 5, because the left - most point is at x=-8 and the right - most point is at x = 5, and the arrows suggest that within that range, the function is defined, and maybe it's a closed interval. Wait, so the domain is ([-8,5]).

Step2: Write the domain in interval notation

Interval notation for all real numbers from - 8 to 5, including both endpoints, is ([-8,5]).

Answer:

([-8,5])