Exeter - Math Teaching Materials 5 - Math-41C-42C-43C-Book-11Aug2017.pdf

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Mathematics 41CMathematics DepartmentPhillips Exeter AcademyExeter, NHAugust 11 2017
Problem Set 1Math 41C1. Big Red Taxi charges a fixed amount of $2.40 plus $3.10 per mile. Big Blue Taxi onlycharges for mileage at a rate of $3.50 per mile. Write equations expressing the amountof the fare as a function of the distance traveled for each of the cabs, and sketch graphsof the functions on the same set of axes.What is common to these two functions?What is different? What can you say about the rate of change of each fare function?2. A college savings account grows at an annual rate of 4.5%. Write an equation expressingthe amount in the accounttyears after an initial deposit of $5000.00, and obtain agraph of the function. Compare this function with the functions in number 1. Howare they similar?How are they different?[Hint: consider what is constant in eachfunction.]3. A functionfis calledevenif it has the property thatf(-x) =f(x) for allx-valuesin the domain. What does this property tell us about the appearance of the graph ofy=f(x) ? Show thatC(x) =2x+2-x2is an even function. Give other examples of evenfunctions.4. A functionfis calledoddif it has the property thatf(-x) =-f(x) for allx-valuesin the domain.What does this property tell us about the appearance of the graphy=f(x)? Show thatC(x) =2x-2-x2is an odd function. Give other examples of oddfunctions.August 11 20171Phillips Exeter Academy
Problem Set 1Math 41C5. Choose from the following equations:y=x2,y=x3,y=x5,y=x4,y=-x,y=x,y=x,y=11/3andy= log(x) todescribe each of the graphs below.x,y= sin(x),y= cosx,y= tan(x),y=x-4-3-2-11234-4-3-2-11234xyFunction A-4-3-2-11234-4-3-2-11234xyFunction B-4-3-2-11234-4-3-2-11234xyFunction C-4-3-2-11234-4-3-2-11234xyFunction D-4-3-2-11234-4-3-2-11234xyFunction E-4-3-2-11234-4-3-2-11234xyFunction FAugust 11 20172Phillips Exeter Academy
Problem Set 1Math 41C6. Choose from the following equations:y=x2,y=x3,y=x5,y=x4,y=-x,y=x,y=x,y=11/3andy= log(x) todescribe each of the graphs below.x,y= sin(x),y= cosx,y= tan(x),y=x-112345-4-3-2-1123xyFunction A-112345-4-3-2-1123xyFunction B-4-3-2-11234-4-3-2-11234xyFunction C-4-3-2-11234-4-3-2-11234xyFunction D-4-3-2-11234-4-3-2-11234xyFunction E-4-3-2-11234-4-3-2-11234xyFunction FAugust 11 20173Phillips Exeter Academy
Problem Set 1Math 41C7. The graph ofy=f(x) is shown below. Write an equation for each of the followinggraphs in terms off(x). For instance, a possible answer could look likey=f(x+2)+3.-4-3-2-1123456789-6-5-4-3-2-1123456xyy=f(x)-4-3-2-1123456789-6-5-4-3-2-1123456xyFunction A-4-3-2-1123456789-6-5-4-3-2-1123456xyFunction B-4-3-2-1123456789-6-5-4-3-2-1123456xyFunction C-9-8-7-6-5-4-3-2-11234-6-5-4-3-2-1123456xyFunction DAugust 11 20174Phillips Exeter Academy
Problem Set 1Math 41C8. The graph ofy=g(x

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Term
Fall
Professor
Mr. Adam Smith
Tags
Derivative, Phillips Exeter Academy

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