Exponential Graph

The exponential graph function with base b is defined by
f(x) = b^x ; 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.

Example :
1) y = b^x , b>1 , the graph will be increasing from right to left in upward direction i.e. from negative x-axis to positive y-axis.
Example :

2) y = - b^x, b<1, the graph will be decreasing right to left in downward direction i.e. from negative x-axis to negative y-axis.
Example :

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.
Example :

4) y = b^x + c ,
first draw a graph of y = b^x as there is + c the graph will be shifted to ‘c’ units up from the graph of y = b^x
Example :

5) y = b^x - c , the graph shifted ‘c’ units down from the graph of y = b^x
Example :

Natural exponential-graph
The function is defined by f(x) = e^x is called the Natural Exponential Function. ( e is an irrational number )

The inverse of the exponential function is the Logarithmic function.

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Exponential graph

Graph Dictionary

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