2) The following data represents the amount of money Tom is saving each month since he graduated from college.

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1 Mac 1 Review for Eam 3 Name(s) Solve the problem. 1) To convert a temperature from degrees Celsius to degrees Fahrenheit, ou multipl the temperature in degrees Celsius b 1.8 and then add 3 to the result. Epress F as a linear function of c. ) The following data represents the amount of mone Tom is saving each month since he graduated from college. month savings $ $70 $81 $91 $ $118 $13 a) Draw a scatter diagram of the data. b) Find the line of best fit using a Graphing Calculator. c) Give a short eplanation on what the slope of the line of best fit represents in this situation. d) Using the line of best fit for the data set, predict the amount Tom ma be able to save in the th month after graduating from college savings month 1

2 Graph the function f b finding the verte, the ais of smmetr, the -intercept and an additional point smmetric to the intercept. Identif the -intercepts if an. 3) f() = Verte: (, Equation of ais of smmetr: -intercept: Point smmetric: -intercepts: Graph the function f b finding the verte, the ais of smmetr, the -intercept and an additional point smmetric to the intercept. Identif the -intercepts if an. ) f() = Verte: (, ) Equation of ais of smmetr: -intercept: Point smmetric: -intercepts: Determine, without graphing, whether the given quadratic function has a maimum value or a minimum value and then find that value. ) f() =

3 6) f() = Determine the quadratic function whose graph is given. 7) Verte: (1, ) -intercept: (0, 3) Solve the problem. 8) The manufacturer of a CD plaer has found that the revenue R (in dollars) is R(p) = -p + 0p, when the unit price is p dollars. a) Find the price p that will maimize the revenue; b) what is the maimum revenue to the nearest whole dollar? 9) A projectile is thrown upward so that its distance above the ground after t seconds is h = -11t + 0t. After how man seconds does it reach its maimum height? What is the maimum height? ) A developer wants to enclose a rectangular grass lot that borders a cit street for parking. If the developer has 316 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? 3

4 11) A coin is tossed upward from a balcon 18 feet high with an initial velocit of 3 feet per second. During what interval of time will the coin be at a height of at least 90 feet? (h = -16t + v0t + h0.) 1) The revenue achieved b selling graphing calculators is figured to be (3-0.) dollars. The cost of each calculator is $. How man graphing calculators must be sold to make a profit (revenue - cost) of at least $1.0? Use a graphing calculator to plot the data and find the quadratic function of best fit. 13) An engineer collects data showing the speed s of a given car model and its average miles per gallon M. Use a graphing calculator to plot the scatter diagram and draw the scatter diagram manuall. What is the quadratic function of best fit? Speed, s mph, M mph speed

5 Graph the function using transformations of the graph of = 3. Indicate the new coordinates of 3 ke points of the basic function. 1) f() = Use transformations of the graph of = to sketch the graph of the function. Indicate the new coordinates of the 3 ke points used to graph =. 1) g() = - ( + ) For the polnomial, list each real zero and its multiplicit. Determine whether the graph crosses or touches the -ais at each -intercept. 16) f() = 3( - )( + 3)

6 Form a polnomial function whose zeros and degrees are given. Use a = 1. Leave the answer in factored form. 17) Zeros: -3, multiplicit ; 1, multiplicit 1;, multiplicit 3; degree = 6 18) For the function f() = (-1)(+)(-3) a) Find the zeros of the function, and indicate their multiplicit. b) Indicate the degree of the polnomial function and identif the power function it resembles for large. c) Find the -intercept. d) Sketch the graph of the function, use a graphing utilit to find the coordinates of the relative maima and minima. e) How man turning points does the graph have. Give the coordinates of the turning points, and indicate the intervals where the function is increasing or decreasing a) Zeros and multiplicities: b) Degree: Resembles = for large c) -intercept: d) Relative maimum : Relative minima ( decimal places): e) # of turning points: Coordinates of turning points: f) Decreasing on:, Increasing on: Construct a polnomial function with the given properties. 19) The graph of the polnomial function crosses the -ais at - and 3, touches the -ais at, crosses the -ais at - and is below the -ais between - and 3. 6

7 Use the figure to solve the inequalit. 0) g() (-, 0) (, 0) Use the graph of the function f to solve the inequalit. 1) f() Solve the inequalit b using the graph of the function. ) f() > 0, where f() = ( + )( - 1)

8 Solve the inequalit. Graph the solution on a number line and write the answer in interval notation. 3) (a + 6)(a - )(a - 7) > 0 Solve the inequalit, then graph its solution. Use interval notation. ( - 1)(3 - ) ) Answer the question. ) Which of the following polnomial functions might have the graph shown in the illustration below? Eplain our answer. A)f() = ( - )( - 1) B)f() = ( - )( - 1) C)f() = ( - )( - 1) D)f() = ( - )( - 1) 8

9 Give the equation of the specified asmptote(s) ) Vertical and Horizontal asmptote(s): f() =, and indicate the domain of f() Equation of Vertical asmptote(s): Domain of f(): Equation of Horizontal asmptote: 7) Horizontal asmptote: h() = Equation of Horizontal asmptote: Graph the function. Find the and the -intercepts (if an), the equations of the vertical and horizontal asmptotes and some ke additional points to sketch the graph of the function. 8) f() = 3 + -intercept: + -intercept: Equation of vertical asmptote: Equation of horizontal asmptote: Additional Points:

10 9) Graph the following function using vertical and horizontal translations of the graph of = 1. Find the equations of the vertical and horizontal asmptote of the new function. 1 f() = Vertical asmptote: Horizontal asmptote: -intercept: -intercept: Additional points:

11 Answer Ke Testname: P308 1) F(c) = 1.8c savings ) month b) Line of best fit: = ; c) The slope is 1.7, it indicates that Tom is saving approimatel $1.7 per month since his college graduation; d) Tom ma be able to save $37.9 in the th month. 3) f() = Verte:(-3,); Ais of smmetr: = -3; -intercept: (0,); Point smmetric: (-6,) -intercepts: (-1,0), (-,0) ) f() = Verte: (,); Ais of smmetr: = -intercept: (0,1); Point smmetric: (,1) -intercepts: { ± }(eact); approimate:{-.,.}

12 Answer Ke Testname: P308 ) minimum; ) maimum; ) f() = Use f() = a -h + k with (h, k) = (1, ) and -int: (0, 3) to get value of a. f() = a > Since -int. is on graph, we have 3 = a > a = -1 --> f() = f() = ) a) Price that will maimize the revenue = $; b) Maimum Revenue = $,1 9) a) Projectile will reach its maimum height after 0 sec; b) Maimum height = 00 feet ) Largest area that can b e enclosed = 1,8 ft 11) Graph 1 = -16t + 3t + 18 and = 90. Use our calculator to determine the time interval in which 1 is greater than. ---> {t 0 t } (set-builder notation); [0, ] (interval notation) 1) Find the Profit function first P() = , then use our calculator to determine whenthe graph of P() is above the graph of = > { 8 < < 3} (set-builder notation); (8, 3) (interval notation) mph 13) M(s) = ) ke points (-1, -1) > (-1, -6) (0, 0) > (0, -) (1, 1) > (1, ) speed

13 Answer Ke Testname: P308 1) ke points: (-1, 1) -----> (-3,1) -----> (-3,-1) ----> (-3, ) (0,0) -----> (-,0) -----> (-, 0) -----> (-, -3) (1, 1) -----> (-1, 1) -----> (-1,-1) ----> (-1, ) ), multiplicit 1, crosses -ais; -3, multiplicit, touches -ais 17) P() = ( + 3)( - 1)( - )3 18) a) -, 3 multiplicit 1, 1 multiplicit b) Degree ; resembles = for large c) -intercept: -6 d) Relative maimum: 0 ; relative mimima: (-1.1, ) and (.0, -.17) e) # of turning points: 3 ; coordinates of turning points: (-1.1, ), (1, 0) and (.0, -.17) f) Decreasing on: (-, -1.1) and (1,.0) Increasing on: ( -1.1, 1) and (.0, ) Graph ) P() = ( 1 30 )( + )( - 3)( - ) 0) { - or } (set-builder notation); (-, -] or [, ) (interval notation) 1) [, ] [6, ) ) (, 1) (1, ) 13

14 Answer Ke Testname: P308 3) (-6, ) or (7, ) ) [1, ) or [3, ) ) D 6) =, = 7) = 8) f() = intercept: (/3, 0); -intercept: (0, /) Vertical Asmptote: = -; Horizontal Asmptote: = 3 Additional points: Find points to the left of the V.A, 1 point between the V.A and the intercept, and 1 point to the right of the -intercept in addition to the -intercept ) f() = V.A: =3 H.A: = - 3 -intercept: (., 0); -intercept: (0, /3) Find the additional points b moving the ke points of = 1/ 3 units to the right, then units up