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8.3 Notes Algebra II Date: ____________________________ I. Vertical and Horizontal Asymptotes Reciprocal Function Parent function: f (x) 1 x Create a table of values: x f(x) -3 -2 -1 0 1 2 3 Type of graph: hyperbola Domain (*limited to values where function is DEFINED): Range: Asymptotes: Intercepts: Even or odd? Not defined: Ex. 1 Limitations on Domain Determine the value(s) of x for which f(x) is not defined. a) f (x) 3 2x 5 b) f (x) 2 x 5x 24 2 Ex. 2 Properties of Rational Functions f (x) 3 x2 Asymptotes: Domain: Range: f (x) 1 1 x2 Asymptotes: Domain: Range: II. Transformations of Reciprocal Functions Parent function: f (x) h-Horizontal Translation a-Orientation and Shape a k xh k-Vertical Translation Ex. 3 Graph Transformations Graph each function. State the domain and range. f (x) 1 3 x 1 x f(x) -3 -2 -1 0 1 2 3 Domain: Range: f (x) x -3 -2 -1 0 1 2 3 Domain: Range: 4 1 x2 f(x) Ex. 4 Writing Equations a) Virgin Airlines has a daily non-stop flight between Los Angeles, California, and Sydney, Australia. A one-way trip is about 7500 miles. i) Write an equation to represent the travel time from Los Angeles to Sydney as a function of flight speed. Then graph the equation. ii) Explain any limitations to the range or domain in this situation. b) A commuter train has a non-stop service from San Francisco to Belmont, a distance of about 25 miles. i) Write an equation to represent the travel time between these two cities as a function of rail speed. Then graph the equation. ii) Explain any limitations to the range or domain in this situation. Assignment: p. 548 #1-11 odd, 25, 29, 49, 51, 57