**What is an Exponential function?**

An exponential function is a function wherein the input variable x occurs as an exponent. A function of the form f(x) = bx + c is considered an exponential function, and also a function of the form f(x) = a is an exponential function.

**Exponential functions**

Suppose b is any number such that and , then an exponential function is a function of the form,

where b is known as a base and x can be any real number.

**Exponential function examples**

f (x) = 2^{x }and g(x) = 5ƒ3^{x} are exponential functions.

The exponential graph of a function represents the exponential function properties.

The graph of function y=2^{x} is shown to below. First, the property of the exponential function graph when the base is greater than 1.

**Exponential function graph 1 **

The graph passes through the point (0,1).

- The domain is all real numbers.
- The range is y>0.
- The graph is increasing.
- The graph is asymptotic to the x-axis as x approaches negative infinity
- The graph increases without bound as x approach positive infinity
- The graph is continuous
- The graph is smooth

**Exponential function graph 2 **

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 includes all real numbers.
- The range is of y>0.
- It forms a decreasing graph
- The line in graph above is asymptotic to the x-axis as x approaches positive infinity.
- The line increases without bound as x approaches negative infinity.
- It is a continuous graph.
- It forms a smooth graph.

**Exponential Series**

**Exponential function in c**

In the C Language, the **exponential function** returns e raised to the power of x.

Syntax

The syntax for the exp function in the C Language is:

double exp(double x);

**Parameters or Arguments – X**

The value used in the calculation where e is raised to the power of x. If the magnitude of x is too large, the exp function will return a range error.

It returns:

The exp function returns the result of e raised to the power of x.

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