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

Which of the following shows  12 and 112 on the number line?