(3) ( ) UNIT #11 A FINAL LOOK AT FUNCTIONS AND MODELING REVIEW QUESTIONS. Part I Questions. = 3 + 2, then 1.

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1 Name: Date: UNIT # A FINAL LOOK AT FUNCTIONS AND MODELING REVIEW QUESTIONS Part I Questions. If a quadratic function, f ( ), has a turning point at (, ), and g( ) f ( ) where does g( ) have a turning point? () ( () (7, (), ) ) (, 7) () ( 7, 7) = +, then. ( ) = + 0 ( ) = ( ) ( ). If f and g f then g =. () 7 () () 0 (). The graph of the function f ( ) is shown below in bold. Which of the following would. give a possible formula for the function g( )? () g( ) = f ( ) f ( ) () g( ) = f ( ) () g( ) = f ( ) () g( ) = f ( ) g ( ). Given the two quadratic functions, ( ) and ( ) f g, shown below, which of the following. equations shows the correct relationship between the two functio g ( ns? ) f ( ) () g( ) = f ( ) () g( ) = f ( ) g = f () ( ) f () g ( ) = ( ) COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0

2 . Which of the following scenarios describes a discrete function?. () The distance an object falls as a function of the time it has been falling. () The height of a mountain as a function of the location along a road. () The wait time for a park ride as a function of the number of people standing in line. () The volume of water in a pool as a function of the time it has been draining. 6. Franco starts with $.0 in his cash bo and sells snow cones for 0 cents each. Which of 6. the following graphs shows the amount of mone in his bo as a function of the number of snow cones he's sold? 6 () () Mone in Cash Bo, $ Mone in Cash Bo, $ () 6 () 6 Mone in Cash Bo, $ Mone in Cash Bo, $ A linear function models the depth of snowfall, in inches, as a function of the number of 7. hours, h, since it started snowing. The equation is d = 0.h+.. We can interpret the equation as telling us () the snow fell at a rate of 0. inches per hour and started at a depth of. inches. () the snow fell at a rate of. inches per hour and started at a depth of 0. inches. () the snow fell at a rate of inch each 0. hours and started at a depth of. inches. () the snow fell at a rate of inch each. hours and started at a depth of 0. inches. COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0 6 8

3 8. An eponential function has values shown in the table below, rounded to the 8. nearest hundredth. If the equation for this eponential function was written in the form = a b, then which of the following is closest to the value of b? ( ) () 0.7 ().8 ().76 () Which of the following is the graph of the function f ( ) () () < = 8? 9. () () + < 0. Given the function f ( ) =, what is its average rate of change over the interval? () 7 () 6 () (). A ball was dropped from the top of a 0 foot tall building. Its height above the ground is. given b the equation h= 0 6.t, where t is the time it has been dropping in seconds. Which of the following gives the time it takes for the ball to reach the ground? (). seconds ().76 seconds ().89 seconds ().09 seconds COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0

4 . A dart arcs through the air such that its height in feet above the ground can be modeled. b the equation = , where represents its horizontal distance along the ( ) ground. What is the maimum height the dart reaches on its path? () 7. ().9 () 8.6 () Free Response Questions. Function f ( ) is shown graphed on the accompaning grid. f ( ) If g( ) = f ( ) then sketch a graph of g( ) on the grid. State the coordinates of the verte of g( ).. The function f ( ) b g( ) = f ( ). is shown below. The function g is defined (a) Evaluate g ( ). Show how ou came up with our answers. (b) What are the zeroes of g( )? Eplain how ou arrived at our values. f ( ). A tet plan charges a base price of $0.00 per month and an additional $0.0 per tet. If represents the cost of the tet plan and represents the number of tets sent then: (a) Write a model for the cost,, as a function of the number of tets,. (b) If the charge for a month of the teting was $.90, then determine algebraicall how man tets were sent. (c) Eplain wh this is an eample of a discrete function. COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0

5 6. The number of likes generated b a social media add are being tracked b an advertising firm. The total likes is shown in the table below as a function of the number of das since the add was first posted. Das Since Posting, 7 0 Number of likes, (a) Create linear and eponential equations of best fit. Round all parameters to the nearest hundredth. Also state the correlation coefficients for both models. Linear: a b Eponential: = a b = + ( ) (b) Eplain wh the eponential model should predict the number of likes better than the linear model? (c) For the eponential model, create a sketch of the residuals produced b this model. Residual 60 (d) Does the pattern of the residuals indicate that the eponential model is appropriate? Eplain? 7 (e) After weeks, the add had generated,07 likes. Would the eponential model from (a) under predict or over predict the number of likes? B how man? 0 COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0

6 7. The per pound price of lobster varies with the weight of the lobster. Generall, the greater the weight of the lobster, the more ou pa per pound for it. Cook's Lobster House has a lobster pricing structure given below: ( ) p w $ w < $7.0 w < = $8. w < $9.0 w where w is the weight of the lobster, in pounds, and p is the price per pound for the lobster. Price Per Pound ($) (a) Graph this function on the aes provided. Weight (pounds) (b) Mart ordered a lobster that weighed in at pounds. How much did he pa for his lobster? Show the work that leads to our answer. 8. On the graph below, sketch the function f ( ) = + 0< 6 (a) Graph f ( ) on the grid. (b) State the range of f ( ). (c) What are the zeroes of this function? COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT # emathinstruction, RED HOOK, NY 7, 0