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