Shifting
a) along the y-axis
The graph of an exponential function is shifted with the parameter $d$ along the y-axis. This changes the asymptote and the value range. The general formula is:
$y=b^x+d$
!
Remember
- If $d > 0$, the graph is shifted up.
- If $d < 0$, the graph is shifted down and gets a zero.
- The asymptote is at $y=d$.
- The range of values is $W=[d,\infty]$
Example
$\color{blue}{f(x)=2^x}$
$\color{green}{g(x)=2^x+2}$
$\color{brown}{h(x)=2^x-2}$
b) along the x-axis
The graph of an exponential function is shifted with the parameter $c$ along the x-axis. The general formula is:
$y=b^{x+c}$
!
Remember
- If $c$ > 0, the graph is shifted to the left and corresponds to a stretch of $b^c$.
- If $c$ < 0, the graph is shifted to the right and corresponds to a compression of $(\frac{1}{b})^c$.
Beispiel
$\color{blue}{f(x)=2^x}$
$\color{green}{g(x)=2^{x+2}}$
$\color{brown}{h(x)=2^{x-2}}$
