Exponentials and Logs

Kathryn Peake, Jun 17, 2016

Table of Contents

  1. Properties of exponential functions
    1. Exponentials and Logarithms
    2. The Exponential Function - gradient
    3. Exponential Functions - gradient when x = 0
    4. Exponential functions and their gradient functions
  2. The Exponential Function and the Natural Logarithm Function
    1. Logarithmic and Exponential functions
  3. Transformations of the Exponential Function
    1. Transformations 1
    2. Transformations 2
    3. Transformations 3
    4. Transformations 4
    5. Transformations 5
    6. Transformations 6
  4. Transformations of the Natural Logarithm Function
  5. Modulus Functions
    1. Modulus functions
  6. Differentiation
    1. Exponential Functions - gradient
    2. Differentiation of Functions
    3. Derivative of exponential and natural log functions

1.

Properties of exponential functions

  • 1. Exponentials and Logarithms
  • 2. The Exponential Function - gradient
  • 3. Exponential Functions - gradient when x = 0
  • 4. Exponential functions and their gradient functions

1.1.

Exponentials and Logarithms

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1.2.

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1.3.

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1.4.

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2.

The Exponential Function and the Natural Logarithm Function

  • 1. Logarithmic and Exponential functions

2.1.

Logarithmic and Exponential functions

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3.

Transformations of the Exponential Function

  • 1. Transformations 1
  • 2. Transformations 2
  • 3. Transformations 3
  • 4. Transformations 4
  • 5. Transformations 5
  • 6. Transformations 6

3.1.

Transformations 1

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3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Transformations of the Natural Logarithm Function


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5.

Modulus Functions

  • 1. Modulus functions

5.1.

Modulus functions

Arrange the elements above into different functions.[br]Try to sketch the graph on paper.[br]Then check your attempt, using the GeoGebra applet above.
– Kathryn Peake

6.

Differentiation

  • 1. Exponential Functions - gradient
  • 2. Differentiation of Functions
  • 3. Derivative of exponential and natural log functions

6.1.

Exponential Functions - gradient

Move the slider,and notice the way the gradient of the function at (0,1) changes as the base of the exponential changes. Make a note of significant relationships. (When is the gradient negative, positive, zero, 1 ...)
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6.2.

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6.3.

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