#### This above function is an example for Exponential growth, meaning, the function is growing very Rapidly after a slow start.

Exponential functions will always have an Asymptote. Here y=0, is an Asymptote.

#### Type II

#### The above function is an example for Exponential decay, where the function reduces rapidly.** The Asymptote for this function is also, y=0**

**Problem**

**Solution**

**Problem**

**Solutions**

**The graph of function y=2 ^{-x} is shown above. The properties of the exponential function and its graph when the base is between 0 and 1 are given.**

**The line passes through the point (0,1)****The Domain consists of all real numbers****The Range consists of all y>0****The Graph represents a decreasing function****The Graph is Asymptotic to the x-axis (y=0)****As x approaches positive infinity, the functions heads to zero****The line increases without bound as x approaches negative infinity****It is a continuous Graph****There are no breaks in the Graph.**

**Questions to think ??**

**Why we dont take the value of a = 1 or any Negative values? Leave your replies in the comment box**

**Solution**

**We have already learned how to graph the function without the presence of 3. In this question the number 3 (it is called the Stretch) will slightly Stretch the Graph from its Original point.**

**Foremost, let us draw the following table for values of x, as follows, and then plot the points for the Graph**

**Domain: All Real Numbers **

Range: All y>0

Also y = 0 , is an Asymptote for the Graph

Range: All y>0

Also y = 0 , is an Asymptote for the Graph

**Question 2**

**As always, let us design the table for this function, taking values for x = -1,0,1,2,3,4**

**Domain: All Real numbers **

Range: All y>0

y=0, will still be an Asymptote for this graph

Range: All y>0

y=0, will still be an Asymptote for this graph

**Try these Questions**

**Problem**

**Solution**

**Try the following questions on Exponential functions**

**Simplify : 2**

^{x}– 2^{x + 1}**Hint: – 2**

^{x}**Simplify: 3**

^{x}+ 2 × 3^{x}+ 2 × 3^{x + 1}**Simplify the following**