Pre-Calculus 12 Notes

By: Gen L.

Lesson 3: Rational Functions and Transformations

Rationals

A Rational Function is a function that can be represented as a fraction of polynomials. ()

Examples include:

Basis Functions

There are two basis functions.

Common Characteristics of basis:

• Restriction:
• Domain:
• Range:
• Asymptotes:

Transformations

Here's our toolkit:

• : Vertical Stretch
• : Horizontal Translation (x-coordinate of central point)
• : Vertical Translation (y-coordinate of central point)

Graphing Transformations

• Note the basis
• Note the central point.

Try sketching a graph of these:

Example 1

• Basis:
• Central Point:
• Restriction:
• Behaviour near Restriction
  • Left:
  • Right:
• End Behaviour:
• Asymptotes:

Example 2

• Basis:
• Central Point:
• Restriction:
• Behaviour near Restriction:
• End Behaviour:
• Asymptotes:

Determining Equations

1. Note the basis
2. Determine the Central Point
3. Determine

• Pick a point on the function
• Plug in values.

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