Exponential functions

An example of an exponential function is

f (x) = 3^{x}

We say that the base of the exponential function is $3.$

Here are a few key values of the function:

\begin{array}{cccccc} x & - 2 & - 1 & 0 & 1 & 2 \\ f (x) & \frac{1}{9} & \frac{1}{3} & 1 & 3 & 9 \end{array}

In this tutorial, we will learn how to sketch exponential curves like $y = 3^{x}$ and deal with some types of exponential equations.

On the same set of axes, sketch the curves

\begin{aligned} y & = 3 \times 3^{x} \\ y & = \frac{\sqrt{3^{x}}}{3} \\ y & = 1 - \frac{1}{3^{x}} \end{aligned}