Answers:
Domain: [ -1, 3 )
Range: ( -5, 4 ]
Be careful about the use of square brackets vs curved parenthesis.
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Explanation:
The domain is the set of all allowed x values of a function. These are the inputs.
The furthest to the left we can go is x = -1. A closed endpoint is here meaning we include this as part of the domain. Unfortunately the other endpoint 3 is not included due to the open hole.
So x is between -1 and 3, including -1 but excluding 3
We can write that as the compound inequality [tex]-1 \le \text{x} < 3[/tex] which then directly translates into the interval notation [ -1, 3 )
The square bracket includes the endpoint -1; in contrast, the curved parenthesis excludes 3
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The range deals with the output y values. It's the set of all possible outputs.
The lowest we can go is y = -5 but we can't actually reach it because of the open hole.
The highest we can go is y = 4 and we can reach this value.
Hence the range as a compound inequality is [tex]-5 < \text{y} \le 4[/tex] and that leads to the interval notation ( -5, 4 ]
Once again, take note of the use of square brackets vs curved parenthesis. This time we're excluding the lower endpoint but including the higher endpoint.
