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Pertanyaan

Jika fungsi begin mathsize 14px style y minus 1 equals open parentheses x plus 2 close parentheses squared end style direfleksikan terhadap titik O(0,0), maka bayangannya adalah ....

  1. begin mathsize 14px style y equals x squared minus 4 x minus 5 end style

  2. begin mathsize 14px style y equals x squared minus 4 x plus 5 end style

  3. begin mathsize 14px style negative y equals x squared minus 4 x minus 5 end style

  4. begin mathsize 14px style negative y equals x squared minus 4 x plus 5 end style

  5. begin mathsize 14px style negative y equals x squared plus 4 x plus 5 end style

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

bayangannya adalah begin mathsize 14px style negative y equals x squared minus 4 x plus 5 end style.

Pembahasan

Ambil suatu titik pada kurva tersebut misalkan titik (x,y) dan direflesikan terhadap titik O(0,0), sehingga kita punya

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x to the power of apostrophe end cell row cell y to the power of apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row x row y end table close parentheses end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses open parentheses x close parentheses plus 0 open parentheses y close parentheses end cell row cell 0 open parentheses x close parentheses plus open parentheses negative 1 close parentheses open parentheses y close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative x plus 0 end cell row cell 0 minus y end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative x end cell row cell negative y end cell end table close parentheses end cell end table end style

Sehingga kita peroleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of apostrophe end cell equals cell negative x rightwards arrow x equals negative x apostrophe end cell row cell y to the power of apostrophe end cell equals cell negative y rightwards arrow y equals negative y apostrophe end cell end table end style

Kemudian, subtitusikan x = -x' dan y = -y' ke fungsi kaudrat tersebut sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus 1 end cell equals cell open parentheses x plus 2 close parentheses squared end cell row cell negative y to the power of apostrophe minus 1 end cell equals cell open parentheses negative x to the power of apostrophe plus 2 close parentheses squared end cell row cell negative y to the power of apostrophe minus 1 end cell equals cell open parentheses x to the power of apostrophe close parentheses squared minus 4 x to the power of apostrophe plus 4 end cell row cell negative y to the power of apostrophe minus 1 plus 1 end cell equals cell open parentheses x to the power of apostrophe close parentheses squared minus 4 x to the power of apostrophe plus 4 plus 1 end cell row cell negative y to the power of apostrophe end cell equals cell open parentheses x to the power of apostrophe close parentheses squared minus 4 x apostrophe plus 5 end cell end table end style

Jadi, bayangannya adalah begin mathsize 14px style negative y equals x squared minus 4 x plus 5 end style.

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