Question

What is the range of this piecewise function

Answer 1

Answer as a compound inequality: $-4 \le y < 2$

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 $y \ge -4$ which is the same as $-4 \le y$

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 $y < 2$

Combine $-4 \le y$ and $y < 2$ to get the compound inequality $-4 \le y < 2$

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.