Pertanyaan

Grafik fungsi f ( x ) = x + r p x + q melalui titik-titik A ( − 4 , 9 ) dan B ( 4 , 1 ) sedangkan asimtot tegaknya adalah x = − 3 . Tentukan nilai p , q , dan r !

Grafik fungsi $f (x) = \frac{p x + q}{x + r}$ melalui titik-titik $A (- 4, 9)$ dan $B (4, 1)$ sedangkan asimtot tegaknya adalah $x = - 3$ . Tentukan nilai $p, q, dan r$ !

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai

adalah

2 space comma space space minus 1 space comma space dan space 3

Pembahasan

Diketahui grafik fungsi melalui titik-titik dan sedangkan asimtot tegaknya adalah . Maka: - Fungsi melalui titik , maka: - Fungsi melalui titik , maka: - Fungsi asimtot tegaknya adalah , maka: - Subtitusi (3) ke (1) - Subtitusi (3) ke (2) - Jumlahkan (4) dan (5) Jadi, nilai adalah .

Diketahui grafik fungsi $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator p x plus q over denominator x plus r end fraction end style$ melalui titik-titik dan sedangkan asimtot tegaknya adalah . Maka:

- Fungsi $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator p x plus q over denominator x plus r end fraction end style$ melalui titik , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell space space space space space space space space space f open parentheses x close parentheses end cell equals cell fraction numerator p x plus q over denominator x plus r end fraction end cell row cell space space space space space space space space space space space space space y end cell equals cell fraction numerator p x plus q over denominator x plus r end fraction end cell row cell space space space space space space space space space space space space space space 9 end cell equals cell fraction numerator p open parentheses negative 4 close parentheses plus q over denominator open parentheses negative 4 close parentheses plus r end fraction end cell row cell space space minus 36 plus 9 r end cell equals cell negative 4 p plus q end cell row cell 4 p minus q plus 9 r end cell equals cell 36 space... space left parenthesis 1 right parenthesis end cell end table$

- Fungsi $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator p x plus q over denominator x plus r end fraction end style$ melalui titik , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell space space space space space space space space f open parentheses x close parentheses end cell equals cell fraction numerator p x plus q over denominator x plus r end fraction end cell row cell space space space space space space space space space space space space y end cell equals cell fraction numerator p x plus q over denominator x plus r end fraction end cell row cell space space space space space space space space space space space space space 1 end cell equals cell fraction numerator p open parentheses 4 close parentheses plus q over denominator open parentheses 4 close parentheses plus r end fraction end cell row cell space space space space space space space space 4 plus r end cell equals cell 4 p plus q end cell row cell 4 p plus q minus r end cell equals cell 4 space... space left parenthesis 2 right parenthesis end cell end table$

- Fungsi $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator p x plus q over denominator x plus r end fraction end style$ asimtot tegaknya adalah , maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow negative 3 of open parentheses x plus r close parentheses end cell equals 0 row cell negative 3 plus r end cell equals 0 row r equals cell 3 space horizontal ellipsis space left parenthesis 3 right parenthesis end cell end table

- Subtitusi (3) ke (1)

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 p minus q plus 9 r end cell equals 36 row cell 4 p minus q plus 9 left parenthesis 3 right parenthesis end cell equals 36 row cell 4 p minus q plus 27 end cell equals 36 row cell 4 p minus q end cell equals cell 9 space horizontal ellipsis space left parenthesis 4 right parenthesis end cell end table

- Subtitusi (3) ke (2)

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 p plus q minus r end cell equals 4 row cell 4 p plus q minus 3 end cell equals 4 row cell 4 p plus q end cell equals cell 7 space horizontal ellipsis space left parenthesis 5 right parenthesis end cell end table

- Jumlahkan (4) dan (5)

table attributes columnalign right center left columnspacing 0px end attributes row cell 8 p end cell equals 16 row p equals 2 row blank blank blank row cell 4 left parenthesis 2 right parenthesis plus q end cell equals 7 row cell 8 plus q end cell equals 7 row q equals cell negative 1 end cell row blank blank blank end table

Jadi, nilai p comma space q comma space dan space r adalah 2 space comma space space minus 1 space comma space dan space 3 .