1.4: Graphs of Basic Functions

Michael Bailey, Feb 23, 2015

Table of Contents

  1. Parent Functions
    1. 5 Basic Functions
    2. Squaring Function
    3. Cubing Function
    4. Absolute Value Function
    5. Square Root Function
    6. Cube Root Function
  2. Transformations
    1. Transfomations
    2. Vertical Stretches and Compressions
    3. Horizontal Stretches and Compressions
    4. Translations
    5. Transformations
  3. Problem 1
    1. Explamples
    2. Problem 1 A)
    3. Problem 1 B)
    4. Problem 1 C)
  4. Problem 2
    1. Examples
    2. Problem 2

1.

Parent Functions

  • 1. 5 Basic Functions
  • 2. Squaring Function
  • 3. Cubing Function
  • 4. Absolute Value Function
  • 5. Square Root Function
  • 6. Cube Root Function

1.1.

5 Basic Functions

We will begin this section by taking a look at the graphs of 5 basic functions. These basic function, or [b]parent functions[/b], are the simplest form in a set of functions that form a family. They will show up over and over again throughout the course, so it is important that we learn their shapes and properties.[br][br]Once we have done so, we will perform [b]transformations[/b] on the equations and graphs of these  basic functions to form other functions in the parents function's family.[br][br]For each function, fill in the table to show the graph. Copy down the table, graph, domain, and range in your notes for future reference.
– Michael Bailey

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

Transformations

  • 1. Transfomations
  • 2. Vertical Stretches and Compressions
  • 3. Horizontal Stretches and Compressions
  • 4. Translations
  • 5. Transformations

2.1.

Transfomations

Next we are going to look at transformations of our basic functions. For any parent function [math]f\left(x\right)[/math], we can graph functions of the form[br][br][center][math]a\cdot f\left(b\left(x+h\right)\right)+k[/math][/center]where [math]a[/math], [math]b[/math], [math]h[/math], and [math]k[/math] will determine different transformations of the parent function, which will include stretches, shrinks, translations, and reflections. [br][br][justify][br][/justify]
– Michael Bailey

2.2.

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2.3.

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2.4.

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2.5.

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3.

Problem 1

  • 1. Explamples
  • 2. Problem 1 A)
  • 3. Problem 1 B)
  • 4. Problem 1 C)

3.1.

Explamples

– Michael Bailey

3.2.

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3.3.

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3.4.

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4.

Problem 2

  • 1. Examples
  • 2. Problem 2

4.1.

Examples

– Michael Bailey

4.2.

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Information