Exponential Functions

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) = 2x and g(x) = 5ƒ3x are exponential functions.

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

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

Exponential Functions

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 Functions

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 Functions

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.

For Complex exponential function and exponential function formula, visit www.byjus.com for detailed explanation.


Practise This Question

There is a unique quadrilateral ABCD possible with AB = 4 cm, BC = 6 cm, AC = 7 cm, CD = 5 cm and BD = 8 cm. State True or False.