There are many quantities like population, compound interest etc. in real life which grow exponentially. So understanding of exponential functions is an essential to deal with such type of things in the real life.
If a>0 and not equal to 1 then the function f:RàR defined by f(x) = ax is called exponential function with base a.
If a is greater than 1, the function continuously increases in value with the increase of x. A special property of exponential functions is that the slope of the function also continuously increases as x increases. Instead of writing ax we can write the same thing as a^x where the symbol ^ is a sign for power. Even in the computer programs and in the calculators this sign is used to represent the powers.
Here, if we restrict the values of a to the positive numbers then the domain will be the set of all real numbers.
The following graph represents the exponential functions f(x) and g(x) where a>1 for f(x) and 0<a<1 for g(x).
Exponential function is a function which is of the form f(x)=ax + b, where x is the exponent or power of a, where a is any constant and b is any expression. Unless, an exponential function is transformed, it always passes through (0,1) (because a0 =1) and does not cross the x-axis (because ax≠0 for any value of x) .
Example:
Graph of 2x.
Solution:
Let us find a table of values by substituting different values for x.
| x | 0 | 1 | 2 | 3 |
| 2x | 1 | 2 | 4 | 8 |
Let us plot the points to get the graph now.
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