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9.2 Graphing Simple Rational Functions Rational Functions Rational Function: is a function of the form p( x) f ( x) q ( x) Hyperbola x -4 -3 -2 -1 1 2 1 2 1 2 3 4 y 1 f ( x) x Rational Functions Hyperbola: the graph of a rational function. The x-axis is a horizontal asymptote The y-axis is a vertical asymptote The domain and range are all nonzero real numbers The graph has two symmetrical parts (branches) Investigation 1) Graph each function. 2 x c) 3 y b) x d) a) 2) 3) y y y 1 x 2 x Use the graphs to describe how the a sign of a affects the graph of y x . Use the graphs to describe how a affects the graph of y a . x Rational Functions (In General) Rational Functions in the form… a y k xh Asymptotes are at… x = h and y = k Examples: Graph the functions and state the domain and range. 1) 2) 3) 3 y 2 x 1 x2 y 3x 3 1 y 3 x4 Examples: 4) The senior class is sponsoring a dinner. The cost of catering the dinner is $9.95 per person plus an $18 delivery charge. a) b) Write a model that gives the average cost per person. Graph the model and use it to estimate the number of people needed to lower the cost of $11 per person. Example (Continue): c) Describe what happens to the average cost per person as the number increases. Example: 4) The speed of sound can be modeled by 1.09F + 1087.8 ft/sec, where F is the temperature in oF. a) b) Write a model that gives the time it takes you to hear thunder a mile away. Graph the model and use it to estimate to how long it takes you to hear the thunder a mile away if it is 75o. Example (Continue) c) Describe what happens to the length of time it takes for the thunder to reach your ears as the temperature decreases.