9 2 Graphing Simple Rational Functions Rational Functions

9. 2 Graphing Simple Rational Functions

Rational Functions ¡ Rational Function: is a function of the form

Hyperbola x -4 -3 -2 -1 1 2 3 4 y

Rational Functions ¡ Hyperbola: the graph of a rational function. l l 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) 2) 3) Graph each function. a) c) b) d) Use the graphs to describe how the sign of a affects the graph of. Use the graphs to describe how affects the graph of.

Rational Functions (In General) ¡ ¡ Rational Functions in the form… Asymptotes are at… x = h and y = k

Examples: Graph the functions and state the domain and range. 1) 2) 3)

Examples: 4) The senior class is sponsoring a dinner. The cost of catering the dinner is $9. 95 person plus an $18 delivery charge. a) b) Write a model that gives the average cost person. Graph the model and use it to estimate the number of people needed to lower the cost of $11 person.

Example (Continue): c) Describe what happens to the average cost person as the number increases.

Example: 4) The speed of sound can be modeled by 1. 09 F + 1087. 8 ft/sec, where F is the temperature in o. F. 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 75 o.

Example (Continue) c) Describe what happens to the length of time it takes for the thunder to reach your ears as the temperature decreases.