Since the Independent variable occurs in the Exponent place, we call such functions as Exponential Functions

We will now Graph this function by taking values for x

When x, takes positive values, the function increases with huge Jumps, but at the same time, when x-takes, negative values, the function reduces to smaller values, but will Never become ZERO.

Connecting all of the points, the Graph will look like this,

The line on the Negative side of the x-Axis, will never touch the axis line, but will forever strive to make contact, such lines are called asĀ Asymptotes

Example 2

Graph this Exponential Function

For this, just draw the graph taking just the exponential function

Now, just shift the graph 3 Units down to handle the negative 3

However the Graph will still have an Asymptote

Example 3

How would you Graph if the Exponent is replaced with, x-3

Solution: just start by graphing the original exponential function

Now, the Graph gets shifted to the right by 3 units

Note that the Graph will still have an Asymptote

Example 4

Now what if the Exponent carries a negative sign

Here you see the graph for the function when the exponent has a positive sign, now to get the graph for the negative exponent, just produce its Mirror image about the y-axis

The Green line is called Exponential Growth: Examples-Profit in Business-Investment growth

The Red line is called Exponential Decay: Examples- Bacterial decay-Radio active elements

Note: All Exponential graphs will have an Asymptote