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Gambarkan grafik fungsi jika daerah asalnya !

Gambarkan grafik fungsi begin mathsize 14px style f open parentheses x close parentheses equals x squared plus 3 x minus 10 end style jika daerah asalnya begin mathsize 14px style negative 1 less or equal than x less or equal than 2 end style!

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Jawaban:

Perhatikan perhitungan berikut ini.

Untuk menggambarkan grafik fungsi begin mathsize 14px style f open parentheses x close parentheses equals x squared plus 3 x minus 10 end style jika daerah asalnya begin mathsize 14px style negative 1 less or equal than x less or equal than 2 end style, maka substitusikan titik batas dari daerah asalnya ke dalam persamaan yaitu:

Untuk begin mathsize 14px style x equals negative 1 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell x squared plus 3 x minus 10 end cell row cell f left parenthesis negative 1 right parenthesis end cell equals cell open parentheses negative 1 close parentheses squared plus 3 open parentheses negative 1 close parentheses minus 10 end cell row cell f left parenthesis negative 1 right parenthesis end cell equals cell 1 minus 3 minus 10 end cell row cell f left parenthesis negative 1 right parenthesis end cell equals cell negative 12 end cell end table end style

Didapatkan begin mathsize 14px style open parentheses negative 1 comma space minus 12 close parentheses end style.

Untuk begin mathsize 14px style x equals 0 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell x squared plus 3 x minus 10 end cell row cell f left parenthesis 0 right parenthesis end cell equals cell left parenthesis 0 right parenthesis squared plus 3 left parenthesis 0 right parenthesis minus 10 end cell row cell f left parenthesis 0 right parenthesis end cell equals cell 0 plus 0 minus 10 end cell row cell f left parenthesis 0 right parenthesis end cell equals cell negative 10 end cell end table end style

Didapatkan begin mathsize 14px style open parentheses 0 comma space minus 10 close parentheses end style.

Untuk begin mathsize 14px style x equals 2 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell x squared plus 3 x minus 10 end cell row cell f left parenthesis 2 right parenthesis end cell equals cell left parenthesis 2 right parenthesis squared plus 3 left parenthesis 2 right parenthesis minus 10 end cell row cell f left parenthesis 2 right parenthesis end cell equals cell 4 plus 6 minus 10 end cell row cell f left parenthesis 2 right parenthesis end cell equals cell 10 minus 10 end cell row cell f left parenthesis 2 right parenthesis end cell equals 0 end table end style

Didapatkan begin mathsize 14px style open parentheses 2 comma space 0 close parentheses end style.

Sehingga dari ketiga titik begin mathsize 14px style open parentheses negative 1 comma space minus 12 close parentheses end stylebegin mathsize 14px style open parentheses 0 comma space minus 10 close parentheses end style, dan begin mathsize 14px style open parentheses 2 comma space 0 close parentheses end style dapat dibuat grafik sebagai berikut:

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