Betty and Stella are in business together making and selling birdhouses. Betty builds birdhouses out of old fence pickets, and Stella sells them in her store. Betty finds that if she has x fence pickets, then the number, N(x), of birdhouses that she is able to build can be approximated by N(x) = 2x 4. One might expect this function to be linear, but Betty's unique carpentry techniques prevent it from being so. Stella determines that the profit, P(x), in hundreds of dollars, that she can earn from the sale of x birdhouses can be approximated by P(x) = 8 220 2x. One might expect this function to be linear as well (or at least polynomial), but Stella's innovative approach to sales prevents it from being so.

1. Find the domain of N.

2. Identify the transformations from the graph of y = x that will produce the graph of y = N(x), then sketch the graph of y = N(x).

3. Use your graph to identify the range of N.

4. Find the domain of P.

5. Identify the transformations from the graph of y = x that will produce the graph of y = P(x), then sketch the graph of y = P(x).

6. According to the function P, what is the largest number of birdhouses that can be sold? How many fence pickets are needed to make this many birdhouses?

7. What function gives the profit that Betty and Stella can earn when given x fence pickets?

8. Use your answers from 1, 3, 4, and 6 to find the domain of the function given in 7. Hint: It is not necessary to write down the function in part 7 to find its domain. You may want to review the definition of a composition of functions in your textbook or notes.

NEED HELP ON QUESTION 7-8 BUT PLEASE ANSWER ALL OF THE QUESTIONS!!! Step by step please