Exponential function : if a is positive real number , then the function which associate every real number x to a^x i.e f(x) = a^x is called the exponential function
Graph exponential function: Here let a >1 , then the exponential function for +ve base is defined as y= f(x) = a^x
Graph of exponential function of y=a^x, a>1
Here in both the above the exponential Function Graph, we can see clearly the domain of the exponential function is R and the range is the set of all positive real number .
Some more graphing exponential functions .
Let us check the graph of y = 3^x
From the graph of y=3^x , we can see that graph is increasing as , x increasing , y is also increasing . Graph of y = 3^x passes through (0,1 ).Domain and range of the graph is set of all real number.The graph of the function is continuos and smooth.
Graph of y=3^x
Graph of y =3^x is decreasing as x decreases the graph of the function decreases. Here the graph passes through (0, 1) and domain of the function is all real number .the graph is smooth and continuos. . The graph is asymptotic to the x-axis as x approaches positive infinity . The graph of the function y= 3^x increases without bound as x approaches negative infinity
**** Followings are the result about exponential functions :-
1. Domain of exponential function is the set of all real number.
2. Range of exponential function is the ser of all +ve number
3. Exponential functions graph always passes through (0,1)
4. Exponentia l function graph is an increasing function as we move from left to right when x increases function also increases.
5. For every large negative values of x , the value of the function approaches 0
Common exponential function
If the base of an exponential function is taken as 10 ,then it is called common exponential function.Thus f(x) = 10^x is common exponential function
Natural exponential function
If the base of an exponential function is taken as e , then it is called natural exponential function.thus f(X) = ex is natural exponential function where.
e = 1+(1/1!)+(2/2!)+(3/3!)+(4/4!)+........... = 2.718(approximately)
Graph of y=ex