Problem 1 (Section 1.1)

A financial department of a company determines that the function below best estimates the price-demand function for selling x thousand laptops.

p(x) = 3960.9x 1x430

a) Write the company's revenue (in millions of dollars) function, R(x).

b) Compute the values of the table for the revenue function you found to the nearest millions of dollars. You do not have to compute the values by hand. Simply write out what you would plug into the calculator.

x (million) R(x) (million $)

1

50

100

150

200

250

300

350

400

c) Plot the points on a graph and connect the points. Clearly label the points, axes, and tick marks for the graph.

Question 2

The function below is a piecewise function.

f(x) = 4x. if 0x15

x+ 10 if 15< x30

1\2 x+ 50 if x >30

Answer each of the questions.

a) Find the following values or explain why we cannot compute them. Clearly show or state the function you are using. You can use a calculator to compute the value.

f(1)

f(0)

f(15)

f(30)

f(50)

b) Roughly sketch the graph of f(x). Make sure to use an appropriate scale for the graph. Label the tick marks on the xaxis and. yaxis.

c) Besides electricity bill rates, what other real-world applications use piecewise functions? Ex-plain how that application fits with a piecewise function.