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REAL LIFE EXAMPLES:Why are composite functions useful?We can use composite functions when one item depends on the other. For instance, if you run a store for a living,the profit your store makes depends on the revenue you intake and also the cost in running that store.Example 3: Jack is shopping for a new coat. He finds a coat that he likes at Marshall Fields that costs$299, but is on sale at a 25% discount. He also has a $20 off coupon on purchases more than $200 thathe can also use on the product.Let p(x) represent the price after the 25% discount: p(x) = x - .25xLet c(x) represent the price after the coupon: c(x) = x – 201. What is the price if you take the discount off first and then take the coupon price off?Find c[p(299)]Example 4: What is the price if you take the coupon price off first and then take the discount price?Find p[c(299)]Based on your conclusions from example 3 and example 4, which is the better deal for YOU as thecustomer?Why would you combine functions in other ways?Carol owns a garden store where she sells birdhouses. The revenue from the sale of the birdhouses isgiven by r(x) = 125x. The function for the cost of making the birdhouses is given by c(x) = 65x + 5400.Her profit p is the revenue minus the cost or p = r – c.So, the profit function p(x) = (r – c)(x)In other words, you can form a new function by performing arithmetic operations on them.Based on your conclusions from above, how many bird houses would Carol have to sell to breakeven?

Example 5 (Word Problem):From 1990 to 1999 the number of births can be modeled by b(x) = -27x + 4103 and the numbers ofdeaths can be modeled by d(x) = 23x + 2164 where x is the number of years since 1990 and b(x) and d(x)are in thousands. The net population P is the number of births per year minus the number of deaths peryear.Write an expression that can be used to model the population increase in the US from 1990 to 1999.Assuming birth and death rates stay the same, estimate the net increase in population in 2010.Group Practice!1) Find (f + g)(x) , (f – g)(x), (f·g)(x) and (f/g)(x) for the following functions:f(x) = x 2 + 2x +3g(x) = x – 4(f + g)(x) (f – g)(x) (f·g)(x) (f/g)(x)2) For each set of ordered pairs find f◦g and g◦f if they exist.f = {(5, -2) (9, 8), (-4, 3), (0, 4)}g = {(3, 7), (-2, 6), (4, -2), (8, 10)}3) Word Problem:There are three temperature scales: Fahrenheit (F), Celsius (C), andKelvin (K). The function K(C) = C + 273 can be used to convert Celsius temperatures to Kelvin. The function C(F)=5/9(F – 32) can be used to convert Fahrenheit to Celsius.Write a composition function that could be used to convert Fahrenheit to Kelvin.