Answer as a compound inequality: [tex]-4 \le y < 2[/tex]
Answer in interval notation: [-4, 2)
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Explanation:
The range is the set of all possible y outputs of a function. When dealing with a graph like this, we just look at the highest and lowest points to determine which y values are possible.
The lowest point occurs when y = -4. We include this value. So far we have [tex]y \ge -4[/tex] which is the same as [tex]-4 \le y[/tex]
The upper ceiling for the y value is y = 2. We can't actually reach this value because of the open hole at (-3,2). So we say that [tex]y < 2[/tex]
Combine [tex]-4 \le y[/tex] and [tex]y < 2[/tex] to get the compound inequality [tex]-4 \le y < 2[/tex]
This says y is between -4 and 2, including -4 but excluding 2.
To convert this to interval notation, we write [-4, 2) where the square bracket says to include the endpoint and the curved parenthesis says to exclude the endpoint.
