Answer:
- Range is -10 < y ≤ 9
- In words: y spans from -10 to 9; exclude -10 but include 9
- Interval notation is (-10, 9]
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Step-by-step explanation
The range is the set of all possible y outputs of a function.
Grab a sheet of paper. Place it horizontally so that it touches the lowest point on the curve. That point appears to be (-2,-10) marked by the open hole. Since we have an open hole here, y = -10 is not part of the range.
Therefore we have y > -10 or -10 < y so far.
Then move the sheet of paper up as high as you can. Keep it horizontal. The highest we can go on this rollercoaster-like curve is (2,9).
This means y = 9 is the largest output possible. We can reach this value because there aren't any open holes at the peak, so y ≤ 9 is another piece we need.
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To summarize: we found that -10 < y and also y ≤ 9
Glue those two items together as one compound inequality, and we end up with the range -10 < y ≤ 9
The outputs span from -10 to 9. We exclude -10, but include 9.
To write this in interval notation, we write (-10, 9]
The curved parenthesis excludes the endpoint, while the square bracket includes the endpoint.