Roboguru

Grafik fungsi  memotong sumbu  di titik . Jika grafik fungsi  digeser ke atas  satuan akan menghasilkan grafik fungsi  yang melalui titik . Tentukan persamaan grafik fungsi .

Pertanyaan

Grafik fungsi f open parentheses x close parentheses equals negative 4 to the power of a minus b x end exponent memotong sumbu Y di titik open parentheses 0 comma space minus 4 close parentheses. Jika grafik fungsi f open parentheses x close parentheses digeser ke atas 3 satuan akan menghasilkan grafik fungsi g open parentheses x close parentheses yang melalui titik open parentheses 1 comma space 1 close parentheses. Tentukan persamaan grafik fungsi g open parentheses x close parentheses.

Pembahasan Soal:

Diketahui grafik fungsi f open parentheses x close parentheses equals negative 4 to the power of a minus b x end exponent memotong sumbu Y di titik open parentheses 0 comma space minus 4 close parentheses. Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell negative 4 to the power of a minus b x end exponent end cell row cell f open parentheses 0 close parentheses end cell equals cell negative 4 to the power of a minus b open parentheses 0 close parentheses end exponent end cell row cell negative 4 end cell equals cell negative 4 to the power of a minus 0 end exponent end cell row cell negative 4 end cell equals cell negative 4 to the power of a end cell row cell negative 4 to the power of 1 end cell equals cell negative 4 to the power of a end cell row 1 equals a row a equals 1 end table 

Diperoleh grafik fungsi f open parentheses x close parentheses equals negative 4 to the power of a minus b x end exponent equals negative 4 to the power of 1 minus b x end exponent. Grafik fungsi f open parentheses x close parentheses digeser ke atas 3 satuan akan menghasilkan grafik fungsi g open parentheses x close parentheses, berarti:

g open parentheses x close parentheses equals negative 4 to the power of 1 minus b x end exponent plus 3 

Grafik fungsi g open parentheses x close parentheses yang melalui titik open parentheses 1 comma space 1 close parentheses. Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals cell negative 4 to the power of 1 minus b x end exponent plus 3 end cell row cell g open parentheses 1 close parentheses end cell equals cell negative 4 to the power of 1 minus b open parentheses 1 close parentheses end exponent plus 3 end cell row 1 equals cell negative 4 to the power of 1 minus b end exponent plus 3 end cell row cell 1 minus 3 end cell equals cell negative 4 to the power of 1 minus b end exponent end cell row cell negative 2 end cell equals cell negative 4 to the power of 1 minus b end exponent end cell row 2 equals cell 4 to the power of 1 minus b end exponent end cell row cell 4 to the power of 1 minus b end exponent end cell equals 2 row cell open parentheses 2 squared close parentheses to the power of 1 minus b end exponent end cell equals cell 2 to the power of 1 end cell row cell 2 to the power of 2 minus 2 b end exponent end cell equals cell 2 to the power of 1 end cell row cell 2 minus 2 b end cell equals 1 row cell negative 2 b end cell equals cell 1 minus 2 end cell row cell negative 2 b end cell equals cell negative 1 end cell row b equals cell fraction numerator negative 1 over denominator negative 2 end fraction end cell row b equals cell 1 half end cell end table 

Jadi, persamaan grafik fungsi g open parentheses x close parentheses adalah g open parentheses x close parentheses equals negative 4 to the power of 1 minus 1 half x end exponent plus 3.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Juli 2021

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