RATIONAL FUNCTIONS Model and graph rational functions You
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RATIONAL FUNCTIONS Model and graph rational functions.
You and your friends go to BJ’s for one of your friends birthday. The total bill comes to $215 including tip. You decide to split it evenly since you all don’t want to get into an argument. How much do each of you pay if there are 18 people? How much do each of you pay if there are 25 people?
Write a function C(x) to represent the amount each person has to pay given x people. What is a reasonable domain and range of this situation? Graph this situation using Desmos and draw a sketch in your notebook. What are the x- and y-intercepts and what do they represent? Describe the shape of the graph in terms of the scenario.
Three of your friends leave before paying their portion. How would we change this function to change this scenario? What is a new reasonable domain and range? Predict how this will change the graph. Sketch this new graph in your notebook.
Why is there no value for this function at 3? We call this a vertical asymptote. Can C(x) ever equal zero? We call this a horizontal asymptote.
Because your waitress was so nice to your group, you decide to each give an extra $2 as a tip. How would we change this function to change this scenario? Does this change my domain or range? Predict how this will change the graph. Sketch this new graph in your notebook.
Did my vertical or horizontal asymptotes change? Why?
