1. State the domain and range.
Explain how the graph of y = (x + 2)2 – 6 can be obtained from the graph of y = x2.
ANSWER
Translate the graph of y = x2 left 2 units and down 6 units.

2. 8.2 Graphing Simple Rational Functions
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

3. Vocabulary: A rational function has the form 𝑓 𝑥 = 𝑝 𝑥 𝑞 𝑥 where 𝑝 𝑥 and 𝑞 𝑥 are polynomials and 𝑞 𝑥 ≠0.
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

4. Steps to graph a rational function:
Find the vertical and horizontal asymptote
Make a table of values with points to the left and the right of the vertical asymptote
Plot points
Connect points with a smooth curve.
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

5. Example: Graph y = 6/x
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

6. Example: Graph y = 4/x
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

7. Note:
The graph of a rational function can be translated vertically and horizontally.
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

8. Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

9. Example: Graph . Vertical Asymptote x = -2 Horizontal Asymptote y = -1-4 1 -3 3 -1 -5
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

10. Example: Graph . Vertical Asymptote x = 1 Horizontal Asymptote y = 2-1
3.5 5 2 3 .5
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

11. Homework: Page 561 #11-13, 17-20
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

12. Warm-Up
Example: Graph

13. Homework Questions

14. Other Rational Functions
All rational functions of the form have graphs that are hyperbolas.
The vertical asymptote of the graph is at x=- d/c.
The horizontal asymptote is the line y = a/c
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

15. Example: Graph . Vertical Asymptote x = -d/c = -(-3)/1 = 3
Horizontal Asymptote y = a/c = 2/1 = 2 X Y 1
-1.5 2 -5 4 9 5
5.5
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

16. Example: Graph . Vertical Asymptote x = -d/c = -(-1)/-1 = -1
Horizontal Asymptote y = a/c = -3/-1 = 3 X Y -3
5.5 -2 8 1 .5
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.

17. Homework: Page # 23,27-30
Essential Question: What does the graph of the rational function y = a/(x-h) look like?
Mastery demonstrated in writing in summary of notes and in practice problems.