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1. Titik sumbu y (x = 0)
2. Asimtot datar ${\displaystyle y={\frac {a}{p}}}$
3. Asimtot tegak penyebut = 0 dengan cari x
4. Harga Ekstrem/Titik balik

${\displaystyle y={\frac {ax^{2}+bx+c}{px^{2}+qx+r}}}$ diubah menjadi ${\displaystyle (yp-a)x^{2}+(yq-b)x+(yr-c)=0}$ lalu cari y dengan menggunakan diskriminan (${\displaystyle D=b^{2}-4ac}$) lalu cari x dengan menggunakan (${\displaystyle x=-{\frac {b}{2a}}}$)

1. Titik potong dengan asimtot datar untuk mencari x dimana y adalah asimtot datar
2. Titik-titik lain

Contoh

• Tentukan ${\displaystyle f(x)\circ g(x)}$ dan ${\displaystyle g(x)\circ f(x)}$ dari ${\displaystyle f(x)=2x+3}$ dan ${\displaystyle g(x)=4x+7}$!

${\displaystyle f(x)\circ g(x)=f(g(x))}$

${\displaystyle f(g(x))=f(4x+7)}$

${\displaystyle f(g(x))=2(4x+7)+3}$

${\displaystyle f(g(x))=8x+17}$

${\displaystyle g(x)\circ f(x)=g(f(x))}$

${\displaystyle g(f(x))=g(2x+3)}$

${\displaystyle g(f(x))=4(2x+3)+7}$

${\displaystyle g(f(x))=8x+19}$

• Tentukan ${\displaystyle f(x)}$ dari ${\displaystyle g(x)=4x+7}$

a ${\displaystyle f(g(x))=8x+17}$!

b ${\displaystyle g(f(x))=8x+19}$!

a

${\displaystyle f(g(x))=8x+17}$

${\displaystyle f(4x+7)=8x+17}$

${\displaystyle f({\frac {4x+7-7}{4}})=8({\frac {x-7}{4}})+17}$

${\displaystyle f(x)=2x-14+17}$

${\displaystyle f(x)=2x+3}$

b

${\displaystyle g(f(x))=8x+19}$

${\displaystyle 4f(x)+7=8x+19}$

${\displaystyle {\frac {4f(x)+7-7}{4}}={\frac {8x+19-7}{4}}}$

${\displaystyle f(x)=2x+3}$

• Tentukan ${\displaystyle f(x)\circ g(x)}$ dan ${\displaystyle g(x)\circ f(x)}$ dari ${\displaystyle f(x)=5x+3}$ dan ${\displaystyle g(x)=x^{2}+4x+7}$!

${\displaystyle f(x)\circ g(x)=f(g(x))}$

${\displaystyle f(g(x))=f(x^{2}+4x+7)}$

${\displaystyle f(g(x))=5(x^{2}+4x+7)+3}$