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I was trying to find the domain and range of the graph . I have found the domain: [-6,4] and the range is [-5,1]. But this doesn't match with the answer. Is it a wrong way to consider the range of the domain and range from the graph directly?

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    so the domain is right? – 2017-02-23
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    Yes your domain is correct – 2017-02-23

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Hints:

Note that the graph is discontinuous at $x=-4$ and that there does not exist $x $ for which $y \in (0,-1] $.

$$\implies \text { Range } = \,\,? $$ $$\implies \text { Domain } = \,\,? $$

Hope you can take it from here.

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    So the range is $(−5,−1)U [0,1)$ and the domain is [-6,4] ? – 2017-02-23
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    @SabbirHasan Yes, you are right. – 2017-02-23