Answer:
- domain: all real numbers
- range: -1 ≤ y ≤ 5 or -1 ≤ y < ∞
Step-by-step explanation:
The arrows on the ends of the graph mean the graph extends indefinitely left and right. The domain is the horizontal extent of the graph, so it extends from -∞ to +∞, all real numbers.
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The upward slant of the graph at the ends is ambiguous regarding the vertical extent of the graph. It could mean either of ...
- the graph oscillates indefinitely between the values -1 and +5, or
- the graph continues upward toward +∞
We expect the latter case would be drawn with the ends of the arrows above the peak value shown. However, oscillation tends to involve a certain symmetry, and the graph has no symmetry about the local minimum points. In short the usual clues to the vertical extent are missing. Your guess is as good as mine.
The range could be [-1, 5], or it could be [-1, ∞). We cannot tell from this graph.
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Additional comment
The shape of the graph does not seem to match that of a 4th-degree polynomial, so we're not at all certain what sort of function is being plotted here. (A 4th-degree polynomial gets steeper beyond the outside zeros, rather than flatter, as shown here.) A couple of different functions with the approximate characteristics shown are graphed in the attachment.
