Daerah hasil fungsi untuk daerah asal adalah ...

Daerah hasil fungsi $begin mathsize 14px style y equals x squared minus 2 x minus 3 end style$ untuk daerah asal $begin mathsize 14px style open curly brackets x vertical line minus 1 less or equal than x less or equal than 4 comma space x element of straight R close curly brackets end style$ adalah ...

$begin mathsize 14px style open curly brackets y vertical line minus 4 less or equal than x less or equal than 0 comma space x element of straight R close curly brackets end style$
$begin mathsize 14px style open curly brackets y vertical line minus 4 less or equal than x less or equal than 11 comma space x element of straight R close curly brackets end style$
$begin mathsize 14px style open curly brackets y vertical line minus 4 less or equal than x less or equal than 5 comma space x element of straight R close curly brackets end style$
$begin mathsize 14px style open curly brackets y vertical line 0 less or equal than x less or equal than 5 comma space x element of straight R close curly brackets end style$
$begin mathsize 14px style open curly brackets y vertical line 0 less or equal than x less or equal than 11 comma space x element of straight R close curly brackets end style$

Jawaban:

$begin mathsize 14px style y equals x squared minus 2 x minus 3 end style$ dengan daerah asal $begin mathsize 14px style open curly brackets x vertical line minus 1 less or equal than x less or equal than 4 comma space x element of straight R close curly brackets end style$

Uji batas interval domain, $begin mathsize 14px style x equals negative 1 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell open parentheses negative 1 close parentheses squared minus 2 open parentheses negative 1 close parentheses minus 3 end cell row blank equals cell 1 plus 2 minus 3 end cell row blank equals 0 end table end style$

Uji batas interval domain, $begin mathsize 14px style x equals 4 end style$

$begin mathsize 14px style y equals 4 squared minus 2 open parentheses 4 close parentheses minus 3 equals 16 minus 8 minus 3 equals 5 end style$

Uji titik puncak

$begin mathsize 14px style x equals negative fraction numerator b over denominator 2 a end fraction equals negative fraction numerator negative 2 over denominator 2 times 1 end fraction equals 1 end style$

$begin mathsize 14px style x equals 1 end style$ termasuk dalam domain, dengan nilai $begin mathsize 14px style y end style$ adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 1 squared minus 2 open parentheses 1 close parentheses minus 3 end cell row blank equals cell 1 minus 2 minus 3 end cell row blank equals cell negative 4 end cell end table end style$

Perhatikan bahwa nilai minimum dari $undefined$ adalah $begin mathsize 14px style y equals negative 4 end style$ dan nilai maksimum $undefined$ adalah $begin mathsize 14px style y equals 5 end style$ . Sehingga daerah hasilnya adalah $begin mathsize 14px style open curly brackets y vertical line minus 4 less or equal than y less or equal than 5 comma space y element of R close curly brackets end style$ .

Jadi jawaban yang tepat adalah C.

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