1. Functions 4 Reciprocal & Rational Functions
Composite & Inverse Functions
Homework
(Haese & Harris, 3rd edition)
Ex 3F Q6 p97
Ex 4G Q1, 4 p129

2. The Reciprocal Function
Reciprocal Functions are functions of the form:
All reciprocal functions hare the same shape
* Vertical Asymptote is found by letting the denominator equal zero.
ie. x = 0
* Horizontal Asymptote is found by allowing x to become very large (both positive and negative)
ie. as as
The reciprocal function is its own inverse, or it is called a
self-inverse

3. Examples

4. Rational Functions y = 0 (x-axis)
Same rules for asymptotes as discussed for the reciprocal function.
Rational Functions of the Form
Rational Functions of the Form
Vertical Asymptote:
Vertical Asymptote:
y = 0 (x-axis)
Horizontal Asymptote:
Horizontal Asymptote:
Example:
Example:
Horizontal Asymptote:
Vertical Asymptote:
Domain:
Range:
Sketch
Horizontal Asymptote:
Vertical Asymptote:
Domain:
Range:
Sketch

5. Composite Functions 3: 1: 2:

6. Inverse Functions
Graphically - The inverse of a function is found by reflecting the function through the line y = x.
You can use the horizontal line test to predict if the inverse function exists If a horizontal line crosses the graph of a function more than once, there is no inverse function.
since the inverse interchanges the x and y values of the function, it also interchanges the domain and range!
Which of the following graphs have inverses that are functions?

7. Graphical Examples of Functions and their Inverses

8. Finding Inverses of Functions Algebraically
Examples: Find the inverses of the following functions: a. b.