The exponential graph function with base b is defined by
f(x) = bx ; where b > 0 , b≠ 1, and x is any real number.
Characteristics of Exponential-Graph:
1) graph crosses the y-axis at (0,1)
2) when b > 1, the graph increases
3) when 0 < b < 1, the graph decreases
4) the domain is all real numbers
5) the range is all positive real numbers (never zero)
6) graph passes the vertical line test ---> it is a function
7) graph passes the horizontal line test ----> its inverse is also a function.
8) graph is asymptotic to the x-axis -----> gets very, very close to the x-axis but does not touch it or cross it.
1) y = bx
, b>1 , the graph will be increasing from right to left in upward direction i.e. from negative x-axis to positive y-axis.
2) y = - bx
, b<1, the graph will be decreasing right to left in downward direction i.e. from negative x-axis to negative y-axis.
3) y = b-x
when the exponent is negative. The graph will be from left to right in upward direction i.e. from positive x-axis to positive y-axis.
4) y = bx
+ c ,
first draw a graph of y = bx
as there is + c
the graph will be shifted to ‘c’ units up from the graph of y = bx
5) y = bx
- c , the graph shifted ‘c’ units down from the graph of y = bx
The function is defined by f(x) = ex
is called the Natural Exponential Function. ( e is an irrational number )
The inverse of the exponential function is the Logarithmic function.