1. 8.2: Graph Simple Rational Functions
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8.2: Graph Simple Rational Functions
2/23/ :24 PM

2. Graphing Simple Rational Functions
Section 8.2

3. 8.2: Graph Simple Rational Functions
The rational function f(x) = 1/x can be transformed by using methods similar to those used to transform other types of functions.
8.2: Graph Simple Rational Functions
2/23/ :24 PM

4. 8.2: Graph Simple Rational Functions
2/23/ :24 PM

5. Domain and Range
The domain is found by making the denominator equal to zero. It is what the restrictions are. Then, set the denominator equal to zero and solve for x.
The range is found by establishing the y-intercept of the graph
In Interval Notation, the domain and range will be from (–∞, x) U (x, ∞) where x represents any holes or vertical asymptotes.
4.4: Rational Functions
2/23/ :24 PM

6. Example 1
Using the graph of f(x) = 1/x as a guide, describe the transformation, graph each function, and determine the domain and range of g(x) = (1/x) – 3 in Interval Notation.
If k = –3, translate 3 units down.
8.2: Graph Simple Rational Functions
2/23/ :24 PM

7. Example 2
Using the graph of f(x) = 1/x as a guide, describe the transformation, graph each function, and determine the domain and range of g(x) = (1/(x + 2))
If h = –2, translate 2 units left.
8.2: Graph Simple Rational Functions
2/23/ :24 PM

8. Example 3
Using the graph of f(x) = 1/x as a guide, describe the transformation, graph each function, and determine the domain and range of g(x) = (–4/(x + 2)) – 1
If k = –1, translate 1 units down.
If h = 2, translate 2 units left.
If a = –4, translate 2 units left.
8.2: Graph Simple Rational Functions
2/23/ :24 PM

9. 8.2: Graph Simple Rational Functions
Your Turn
Using the graph of f(x) = 1/x as a guide, describe the transformation, graph each function, and determine the domain and range of g(x) = (1/(x – 3)) + 2
8.2: Graph Simple Rational Functions
2/23/ :24 PM

10. 8.2: Graph Simple Rational Functions
Assignment
Page 561
11-23 ALL: DO NOT GRAPH; Label the domain and range of each function.
8.2: Graph Simple Rational Functions
2/23/ :24 PM