Math 142 Week-in-Review #1 (Sections A.8, 1.0, 1.1 topics, 1.2 topics, and 1.3)

Transcription

1 Math 142 WIR, copyright Angie Allen, Spring Math 142 Week-in-Review #1 (Sections A.8, 1.0, 1.1 topics, 1.2 topics, and 1.3) 1. Classify each of the following as a power function, rational function, polynomial function (state its degree and leading coefficient), or none of these (state why). a) f(x)=2 x b) g(x)=3x 5 4x 2 6 c) d) h(x)= 3x2 9x+5 x 13 2 e) j(x)=4x 7 x 5 + 2x 1/3 + 2 f) k(x)= 8x2 4 x+2 5x 9 23x g)

2 Math 142 WIR, copyright Angie Allen, Spring Suzie s class is holding a Valentine s Day Fundraiser in which the students are selling boxes of red, heartshaped cookies at the school store next Saturday from 8am-5pm. As an incentive, Suzie s teacher is going to give the students prize points they can use to purchase items from the school store based on the number of hours they work at the fundraiser that day. For the first 3 hours they work, they will get 20 points/hour. For the next 2 hours, they will receive 40 points/hour, and any additional hours they work they get 60 points/hour. Write a function, V(x), for the number of prize points a student will receive for working x hours at the fundraiser. 3. Brooke and Reid own a flower shop. If they charge $39 for an arrangement, they can sell 32 arrangements each week. If they increase the price by $18 per arrangement, they only sell 26 arrangements each week. The girls have determined that they have weekly fixed costs of $900, and it costs them $15 to make each arrangement. Answer the following (assuming demand is linear): a) What price should they charge in order to break-even, assuming they sell at least 12 floral arrangements? b) What price should they charge to maximize their profit?

3 Math 142 WIR, copyright Angie Allen, Spring Find the domain of the following functions. Write your answers using interval notation. a) f(x)=x 2 5x+π b) f(x)= x 2 1 x x+9 c) f(x)= 3 5 x e x x 3 d) f(x)= e x+9 5 x+1 e) f(x)= 4 x+7 2 x 3

4 Math 142 WIR, copyright Angie Allen, Spring x+ 6 x f) f(x)= 4x 2 16 g) f(x)= x+2 e 3x 7 x x+1 x 3 x 2 9 x 1 1<x<1 x>1 5. A piece of office equipment was purchased in 2010 for $3,000 and depreciates linearly over the next 8 years. If the equipment has a scrap value of $600, what will it be worth in 2016? What is the rate of depreciation?

5 Math 142 WIR, copyright Angie Allen, Spring Evaluate the difference quotient f(a+h) f(a) h for the function f(x)= 1 and simplify your answer. 2x 3 7. Solve the following for x: a) 9 x2 1 1=0 3 4x b) 4 x x x 4x+4 x+1 = 0

6 Math 142 WIR, copyright Angie Allen, Spring The quantity demanded of a certain brand of computers is 300/wk when unit price is $450. For each decrease in unit price of $30, the quantity demanded increases by 100 units. The company will not supply any computers if the unit price is $250 or lower. However, they will supply 375 computers if unit price is $325. a) Find the equilibrium point (round to the nearest integer if necessary). b) Find the number of units demanded when revenue is maximized, as well as the price. 9. Rewrite the function k(t)= t2 + t 6 3 t+ 5 as a piecewise function, and find its domain.

7 Math 142 WIR, copyright Angie Allen, Spring Bob can invest in account A which has a nominal interest rate of 7.1% compounded quarterly or in account B which has a nominal rate of 6.2% compounded continuously. Which should Bob choose to maximize his investment? 11. Starting with the basic function f(x)= x, write and graph the function, g(x), that results from shifting f(x) left 3 units, expanding vertically by a factor of 2, reflecting about the x-axis, and then shifting up 4 units.

8 Math 142 WIR, copyright Angie Allen, Spring Graph the following piecewise-defined function, and find its domain. y x x<1 f(x)= 4 x=3 x 1 x>3 x 13. Bill and Sue want to have $50,000 available to give their new granddaughter when she turns 18. They are considering two accounts. Account A earns interest at an annual rate of 8.1% compounded semiannually, and account B earns an annual rate of 8% compounded continuously. Find the least amount of money they would have to invest to reach their goal.

9 Math 142 WIR, copyright Angie Allen, Spring ( 3x 2 y Simplify the following expression leaving no negative exponents: x 4 z 3 ) The population of a small country in 2010 was 50, 000. If the country s population is increasing continuously at a relative rate of 0.15% per year, find the population in 2020 (round to the nearest integer if necessary). 16. An account with $2,000 earns interest at an annual rate of 8%. Find the amount in the account after 10 years if the compounding is a) weekly b) monthly c) continuous