Explain what it means for a function to be (1) and give an example of such a function.

The following two functions have a common input, year t: R gives the average price, in dollars, of a gallon of regular unleaded gasoline, and P gives the purchasing power of the dollar as measured by consumer prices based on 2010 dollars. (a) Using function notation, show how to combine the two functions to create a new function giving the price of gasoline in constant 2010 dollars R(tdollars gallon (RP(t dollars gallon 2010 dollars P(t) dollars (at pump) R(t) dollars. P(tdollars (at pump) 2010 dollars (R P)(t) 2010 dollars gallon gallon Rit dollars . Pt dollars (at pump) 2010 dollars (R P(t dollars gallon gallon OR(t) dollars gallon 2010 dollars P(t) 2010 dollars gallon P(t) dollars (at pump) (R OR(t)dollars gallon 2010 dollars P(t) dollars (at pump) = (R + P)(t 2010 dollars gallon (b) What are the output units of the new function? O2010 dollars per gallon Odollars per gallon gallons per dollar 2010 dollars per dollar (at pump) Ogallons per 2010 dollar

Square cuts of the same size are cut from a flat rectangular piece of cardboard. The remaining cardboard is folded into a lidless box. Assume that the cardboard originally measures 15 inches by 10 inches. Let be the length of one side of the square-cut (at this point you should stop and draw a picture). (A) Write a function describing the volume of the resulting box in terms of x. V(x)=  cubic inches (B) What is an appropriate domain for the volume function? ≤ x ≤  (C) Now write a function describing the surface area of the box in terms of x.  S(x)=  square inches

At a local bank, when you open an account, you provide certain information that is stored in the bank's records. The table below shows the names and mailing zip codes of some of the bank's customers.        (a) Suppose F is the rule that takes a customer's name and provides their mailing zip code. According to the information in this table, is F a function? Explain your reasoning.        (b) Suppose G is the rule that takes a customer's mailing zip code and provides their name. According to the information in this table, is G a function? Explain your reasoning.         (c) If the bank is looking for a way to identify specific customers, why would using their zip code not be a good way to do this? What other input might the bank use instead?