Standaardfuncties en transformaties

a

\(y=3^x\)
\(\downarrow \text{translatie}(2, 3)\)
\(y=3^{(x-2)}+3=3^{x-2}+3\)

1p

\(\downarrow \text{verm. y-as, }-\frac{1}{4}\)
\(f(x)=3^{(-4x)-2}+3=3^{-4x-2}+3\)

1p

\(D_f=\R \) en \(B_f=⟨0, \rightarrow ⟩\)
\(\downarrow \text{translatie}(2, 3)\)
\(D_f=\R \) en \(B_f=⟨3, \rightarrow ⟩\)
\(\downarrow \text{verm. y-as, }-\frac{1}{4}\)
\(D_f=\R \) en \(B_f=⟨3, \rightarrow ⟩\)

1p

Asymptoot \(y=0\)
\(\downarrow \text{translatie}(2, 3)\)
Asymptoot \(y=3\)
\(\downarrow \text{verm. y-as, }-\frac{1}{4}\)
Asymptoot \(y=3\)

1p

a

\(y={1 \over x}\)
\(\downarrow \text{verm. x-as, }-2\)
\(y=-2⋅({1 \over x})={-2 \over x}\)

1p

\(\downarrow \text{verm. y-as, }-\frac{1}{5}\)
\(f(x)={-2 \over (-5x)}={2 \over 5x}\)

1p

\(D_f=\R \begin{Bmatrix}0\end{Bmatrix}\) en \(B_f=\R \begin{Bmatrix}0\end{Bmatrix}\)
\(\downarrow \text{verm. x-as, }-2\)
\(D_f=\R \begin{Bmatrix}0\end{Bmatrix}\) en \(B_f=\R \begin{Bmatrix}0\end{Bmatrix}\)
\(\downarrow \text{verm. y-as, }-\frac{1}{5}\)
\(D_f=\R \begin{Bmatrix}0\end{Bmatrix}\) en \(B_f=\R \begin{Bmatrix}0\end{Bmatrix}\)

1p

Asymptoten \(x=0\) en \(y=0\)
\(\downarrow \text{verm. x-as, }-2\)
Asymptoten \(x=0\) en \(y=0\)
\(\downarrow \text{verm. y-as, }-\frac{1}{5}\)
Asymptoten \(x=0\) en \(y=0\)

1p

a

\(y=\sin(x)\)
\(\downarrow \text{verm. x-as, }5\)
\(y=5⋅\sin(x)=5\sin(x)\)

1p

\(\downarrow \text{translatie}(2, 4)\)
\(f(x)=5\sin((x-2))+4=5\sin(x-2)+4\)

1p

\(D_f=\R \) en \(B_f=[-1, 1]\)
\(\downarrow \text{verm. x-as, }5\)
\(D_f=\R \) en \(B_f=[-5, 5]\)
\(\downarrow \text{translatie}(2, 4)\)
\(D_f=\R \) en \(B_f=[-1, 9]\)

1p

Evenwichtsstand \(y=0\)
\(\downarrow \text{verm. x-as, }5\)
Evenwichtsstand \(y=0\)
\(\downarrow \text{translatie}(2, 4)\)
Evenwichtsstand \(y=4\)

1p

a

\(y={}^{4}\!\log(x)\)
\(\downarrow \text{translatie}(-4, -5)\)
\(y={}^{4}\!\log((x+4))-5={}^{4}\!\log(x+4)-5\)

1p

\(\downarrow \text{verm. y-as, }-\frac{1}{3}\)
\(f(x)={}^{4}\!\log((-3x)+4)-5={}^{4}\!\log(-3x+4)-5\)

1p

\(D_f=⟨0, \rightarrow ⟩\) en \(B_f=\R \)
\(\downarrow \text{translatie}(-4, -5)\)
\(D_f=⟨-4, \rightarrow ⟩\) en \(B_f=\R \)
\(\downarrow \text{verm. y-as, }-\frac{1}{3}\)
\(D_f=⟨\leftarrow , 1\frac{1}{3}⟩\) en \(B_f=\R \)

1p

Asymptoot \(x=0\)
\(\downarrow \text{translatie}(-4, -5)\)
Asymptoot \(x=-4\)
\(\downarrow \text{verm. y-as, }-\frac{1}{3}\)
Asymptoot \(x=1\frac{1}{3}\)

1p

a

\(y=x^6\)
\(\downarrow \text{translatie}(-1, -2)\)
\(y=(x+1)^6-2=(x+1)^6-2\)

1p

\(\downarrow \text{verm. y-as, }\frac{1}{5}\)
\(f(x)=((5x)+1)^6-2=(5x+1)^6-2\)

1p

\(D_f=\R \) en \(B_f=[0, \rightarrow ⟩\)
\(\downarrow \text{translatie}(-1, -2)\)
\(D_f=\R \) en \(B_f=[-2, \rightarrow ⟩\)
\(\downarrow \text{verm. y-as, }\frac{1}{5}\)
\(D_f=\R \) en \(B_f=[-2, \rightarrow ⟩\)

1p

Top \((0, 0)\)
\(\downarrow \text{translatie}(-1, -2)\)
Top \((-1, -2)\)
\(\downarrow \text{verm. y-as, }\frac{1}{5}\)
Top \((-\frac{1}{5}, -2)\)

1p

a

\(y=\sqrt{x}\)
\(\downarrow \text{verm. x-as, }2\)
\(y=2⋅\sqrt{x}=2\sqrt{x}\)

1p

\(\downarrow \text{translatie}(1, 5)\)
\(f(x)=2\sqrt{(x-1)}+5=2\sqrt{x-1}+5\)

1p

\(D_f=[0, \rightarrow ⟩\) en \(B_f=[0, \rightarrow ⟩\)
\(\downarrow \text{verm. x-as, }2\)
\(D_f=[0, \rightarrow ⟩\) en \(B_f=[0, \rightarrow ⟩\)
\(\downarrow \text{translatie}(1, 5)\)
\(D_f=[1, \rightarrow ⟩\) en \(B_f=[5, \rightarrow ⟩\)

1p

Randpunt \((0, 0)\)
\(\downarrow \text{verm. x-as, }2\)
Randpunt \((0, 0)\)
\(\downarrow \text{translatie}(1, 5)\)
Randpunt \((1, 5)\)

1p