Question

determine the domain of the following graph:
answer attempt 1 out of 2
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∅ or ∪ ∞ < > ≤ ≥ , ,) (, (,) all real numbers

Explanation:

Step1: Identify the leftmost x - value

The graph starts at \(x = 0\) (the point on the y - axis, which has \(x = 0\)) and we also look at the endpoints. Wait, actually, looking at the graph, the left - most defined point (the starting point of the graph) has \(x = 0\)? Wait, no, the graph has a point at \(x = 0\) (the blue dot on the y - axis) and another blue dot at \(x = 8\). Wait, let's check the x - coordinates of the endpoints. The graph starts from \(x = 0\) (the point where it touches the y - axis, with a closed dot) and ends at \(x = 8\) (closed dot at \(x = 8\))? Wait, no, looking at the graph, the left - most part: the graph comes from the bottom, crosses the y - axis at \(x = 0\) (closed dot) and then has a curve, and then at \(x = 8\) there is a closed dot. Wait, actually, the domain is the set of all x - values for which the graph is defined. So we need to find the minimum and maximum x - values. The left - most x - value (the smallest x) where the graph exists is \(x = 0\) (since the graph starts at \(x = 0\) with a closed dot) and the right - most x - value is \(x = 8\) (closed dot at \(x = 8\))? Wait, no, wait the graph: let's see the x - axis. The graph has a point at \(x = 0\) (the y - intercept, closed dot) and then goes to \(x = 8\) (closed dot). Wait, but also, between \(x = 0\) and \(x = 8\), the graph is defined. Wait, maybe I misread. Wait, the graph: the left - most x is \(0\) (because the graph starts at \(x = 0\), the closed dot on the y - axis) and the right - most x is \(8\) (closed dot at \(x = 8\)). So the domain is from \(x = 0\) to \(x = 8\), including both endpoints. So in interval notation, that is \([0,8]\). Wait, let's confirm: the domain of a graph is all the x - values that the graph covers. So we look at the leftmost and rightmost points. The leftmost point (smallest x) is at \(x = 0\) (closed dot, so included) and the rightmost point (largest x) is at \(x = 8\) (closed dot, so included). So the domain is \(0\leq x\leq8\), which in interval notation is \([0,8]\).

Step2: Write the domain in interval notation

Since the graph starts at \(x = 0\) (inclusive, because of the closed dot) and ends at \(x = 8\) (inclusive, closed dot), the domain is the interval from \(0\) to \(8\), including both endpoints. So the interval notation is \([0,8]\).

Answer:

\([0, 8]\)