Pre-Calculus 12 Notes

By: Gen L.

Lesson 3: Stretches

Vertical Stretch

• A transformation that changes the distance of the point from the x-axis (). This does change the shape of the graph.
• Scale Factor: the value is multiplied by to change the distance.
  • Case I: , compresses the values.
  • Case II: , stretches the values.
  • Case III: , no stretch.

On

• This means a vertical stretch by a factor of .

or

Example:

For the graph , sketch and .

Values:

Invariant Points

• Like reflections, stretches have Invariant Points as well.
• For Vertical Stretches, are invariant.
• In the previous Example, B and D are invariant.

Horizontal Stretch

• A transformation that changes the distance of the point from the y-axis (). This does change the shape of the graph.
• Scale Factor: the value is multiplied by to change the distance.
  • Case I: , stretches the values.
  • Case II: , compresses the values.
  • Case III: , no stretch.
• So it's opposite of ? Yes!

On

• This means a vertical stretch by a factor of .

Example:

For the graph , sketch and .

Values:

Invariant Points

• For Horizontal Stretches, are invariant.
• In the previous Example, the y-intercept is Invariant.

Notes on Shorthand:

• : Horizontal Stretch
• : Vertical Stretch
• and : Reflections
• and : Horizontal Translation
• and : Vertical Translation

Mapping Notation:

• Determine the Mapping Notation of for these cases:
  • General form?

Answers:

Going Backwards

• Determine an equation for in terms of (form: )

1. , is Invariant.
2. ,

Answers:

Challenge:

What would the following functions look like if they have been ?

Answers:

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