# 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.

**Exponential graph**

Graph Dictionary

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Graph Dictionary

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