GRADE DISTRIBUTION 1 st 4 th 7 th

GRADE DISTRIBUTION 1 st 4 th 7 th 9 th A B C D F No Shows 100+ Range Avg 1/21/2022 10: 50 AM 8. 2: Graph Simple Rational Functions 1

Section 8. 2

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. 1/21/2022 10: 50 AM 8. 2: Graph Simple Rational Functions 3

RATIONAL FUNCTIONS 1/21/2022 10: 50 AM 8. 2: Graph Simple Rational Functions 4

DOMAIN AND RANGE A. 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. B. The range is found by establishing the y-intercept of the graph C. In Interval Notation, the domain and range will be from (–∞, x) U (x, ∞) where x represents any holes or vertical asymptotes. 1/21/2022 10: 51 AM 4. 4: Rational Functions 5

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. 1/21/2022 10: 51 AM 8. 2: Graph Simple Rational Functions 6

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. 1/21/2022 10: 51 AM 8. 2: Graph Simple Rational Functions 7

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. 1/21/2022 10: 51 AM 8. 2: Graph Simple Rational Functions 8

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 1/21/2022 10: 51 AM 8. 2: Graph Simple Rational Functions 9

ASSIGNMENT Page 561 11 -23 ALL: DO NOT GRAPH; Label the domain and range of each function. 1/21/2022 10: 51 AM 8. 2: Graph Simple Rational Functions 10