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Section 1.1: Functions from an Algebraic Viewpoint
#1. (s. 1.1, #32) The total weekly revenue earned at Royal Ruby Retailers is given by R ( p ) = − 34 p^2 + 80 p, where p is the price (in dollars) RRR charges per ruby. Use this function to determine… a. The weekly revenue, to the nearest dollar, when the price is set at $20/ruby,
b. The weekly revenue, to the nearest dollar, when the price is set at $200/ruby (interpret your result).
c. The price RRR should charge in order to obtain a weekly revenue of $1200.
#2. Let f(x) = (^) x^1 + 4. Find…a) f(x 2 ) b) f(x 2 + 1) c) f(x 2 ) + 1
#3. Suppose f(x) = 4 – 2x − 3x 2. Find the following. a. f(0) b. f(–2) c. f(x + h) d. f(x + h) – f(x) h
#4. (s. 1.1, #28) Scientific Research The number of research articles in Physics Review that were written by researchers in the U.S. from 1983 through 2003 can be approximated byhundred articles, where t is time in years since 1983. A ( t ) = −0_._ 01 t^2 + 0_._ 24 t + 3_._ 4 a. Find an appropriate domain of A. Is t ≤ 20 an appropriate domain? Why or why not?
b. Compute A (10). What does the answer say about the number of research articles?
#5. (s. 1.1, #40) Dental Plans A company pays for its employees’ dental coverage at an annual cost C given by C ( q ) = 1000 + 100 q , where q is the number of employees covered and C ( q ) is the annual cost in $. a. If the company has 100 employees, find its annual outlay for dental coverage.
b. Assuming that the government subsidizes coverage by an annual dollar amount of calculate the net cost function N ( q ) to the company, and calculate the net cost of subsidizing its S ( q ) = 200 q, 100 employees. Comment on your answer.
