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Exponential Functions

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Title: Exponential Functions


1
Exponential Functions
2
x y
0 1
1 2
2 4
-1 1/2
-2 1/4
3
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4
Properties of the Exponential Function
  • The domain is .
  • 2. The range is (0, ).
  • 3. It passes through (0, 1).
  • 4. It is continuous everywhere.
  • .

5
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6
 the term exponential function describing
the natural exponential function ex  where e is
Euler's number, a number (approximately
2.718281828)
7
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8
The logarithm of x to the base b is defined by
9
Properties of the logarithmic Function
  • The domain is (0, ) .
  • The range is
  • 3. It passes through (1, 0).
  • 4. It is continuous everywhere.
  • .

10
Laws of Logarithms
Common Logarithm
Natural Logarithm
11
Graphs of Logarithmic Functions
Ex.
y
y
(0, 1)
(0, 1)
x
x
(1,0)
(1,0)
12
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