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We can introduce another parameter $k$ into the definition of the exponential function, giving us two dials to play with.

If we call this parameter $k$, we can write our exponential function $f$ as $$f(x)=b^.$$ You can explore the influence of both parameters $b$ and $k$ in the following applet. You can change the parameters $b$ and $k$ by typing new values in the corresponding boxes.

We can still get the full range of functions if we eliminate either $b$ or $k$. For example, you can see that the function $f(x)=3^$ ($k=2$, $b=3$) is exactly the same as the function $f(x)=9^x$ ($k=1$, $b=9$).To change the value of $f(0)$, you can allow scaling of the function by clicking the corresponding checkbox.Then, the function changes to $f(x)=c b^$ with an additional parameter $c$ that scales (multiplies) the whole function so that $f(0)=c$.You can change the value of $c$ by dragging the red point.You can change range of the $x$ and $y$-axes buttons labeled $x $, $x-$, $y $, and $y-$.