Question

The graph of the piecewise function f(x) is shown.

Answer 1

Answer:  [A]:  The domain is:
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    {x | 1 ≤ x < 5}  .
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Note:  The answer choices given for "A" and "B" are the same;  you meant to type:
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  [A]:   {x | 1 ≤ x < 5}  ;
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  [B]:   {x | 1 < x < 5} ;
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 I know this from the answer choices given in the "image/figure" you have attached.   Since:  " {x | 1 ≤ x < 5} "
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   is the correct answer, I just need to remind you to be sure to know that the 
               "  ≤ " is the appropriate sign.
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Answer 2

First of all, it asks for domain, which is allowed x values.

So immediately we can rule out last 2 answer choices.

If you look at the graph, the allowed x values are from 1 to 5.

Note: closed circle means that number is included and open circle means that number is NOT included

Now we see that 1 has closed circle so 1 is included and there is an open circle at 5, so 5 is NOT included.

Correct domain is {x | $1\leq x$.

ANSWER: Domain is {x | $1\leq x$