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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Warm-Up Example: Graph

Homework Questions

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.

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.

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.

Homework: Page 561-562 # 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.