1) State whether the following are functions and give an explanation for your reason. Give the domain and range for each relation.

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1 MCF M Calc Questions:,,, 7, 8, 9,,,, QUADRATIC FUNCTIONS ) State whether the following are functions and give an eplanation for your reason. Give the domain and range for each relation. a) - 7 b) y c) y d) 8 e) 7 f) ) Given f() = + and g() = + find the values of: a) f() b) g(-) c) f() + g() d) f(g()) ) Sarah is diving into a pool off of a diving board. The graph below represents her height above the water over a period of time. The graph ends at the instant that Sarah begins to swim to the surface of the pool. Height (m) Sarah's Dive Time (s) a) What are the coordinates of the verte and what do these values mean? b) What are the coordinates of the y- intercept. What does this value mean? c) What are the values of the zeros? What do these values represent? d) How deep did Sarah dive? e) What is the domain and range of this quadratic relationship? What do the domain and range represent in this situation? f) Write the equation for this quadratic function in Verte Form, Standard Form, and Factored Form. Hint: Find equation in Verte Form first by using the coordinates of the verte and another point. From there you can epand to Standard Form and factor into Factored Form.

2 ) The manager of a fork factory wants to maimize the profit of the company. He has found a profit function of : P() = where P represents the profit for one year and represents the number of forks produced in thousands. a) Enter the equation in your graphing calculator and graph the function. You will have to change the window to Xmin =, Xma =, Ymin = -, Yma =. b) State the coordinates of the verte and eplain what the values mean. c) State the values of the zeros and eplain what they mean. d) State the domain and range of this function. ) For each quadratic in factored form, state the coordinates of the zeros and the coordinates of the verte. a) y=( - )( + ) b) y=- ( )( 7) c) y=. ( + 7)( + ) ) Epand the following a) ( - ) b) ( + )( 7) c) ( - )( ) d) ( + )( 8)( + ) 7) Factor the following a) a + b) k + k + c) b - 8 d) - e) + - f) + - g) h) - 8) Determine the roots of each equation a) = b) + = - c) = - 9) For the following equations: i) Factor ii) Find the coordinates of the verte. iii) State whether the function has a maimum or minimum a) y = 9 + b) y = c) h = t + ) A quadratic has zeros at (-, ) and (7, ) and passes through point (-, ). Write the equation for the quadratic in factored form and standard form. ) For the following equations: i) Complete the Squares ii) State the coordinates of the verte. iii) State whether the function has a maimum or minimum iv) Graph the function a) y = b) y = c) y = ) State the number of zeros by completing the squares and looking at the equation in verte form. Repeat the eercise by determining the number of zeros using the discriminant. a) y = 8 b) y = - 8 ) A football is kicked into the air from the ground. It s height in metres at t seconds is given by h(t) = -.8t +.t. a) What is the maimum height of the football? b) When does the football hit the ground? c) What is the domain and range of this function? ) A stone is thrown into the air from a bridge over a river. The stone falls into the river. The height of the stone, h meters, above the river t seconds after the stone is thrown, is given by the equation h(t) = -t + t + 7. a) How high is the bridge above the river? b) Determine the maimum height of the stone above the water. c) How long does it take the stone to reach its maimum height? d) When does the stone hit the water? e) State the domain and range for this function.

3 ) In one study the efficiency of photosynthesis in an Antarctic species of grass was investigated. Table below lists results for various temperatures. The temperature is in degrees Celsius and the efficiency y is given as a percent. The purpose of the research was to determine the temperature at which photosynthesis is most efficient. (Source: D. Brown and P. Rothery, Models in Biology: Mathematics, Statistics and Computing.) (ºC) y(%) a) Graph the data on the TI- 8 and determine the equation for the curve of best fit. b) State the domain and range of this function. c) Use the graphing calculator to find the zeros of this function. What do the zeros represent? d) At what temperature is photosynthesis most efficient? e) Use the curve of best fit and your TRACE button on the graphing calculator to determine the percent efficiency of photosynthesis at a temperature of 9 degrees Celsius? f) At what temperature(s) is the efficiency closest to %? EXPONENTIAL FUNCTIONS ) Given the following table of values: a) Determine if the function is linear, quadratic or eponential. b) State the domain and range of the function. c) If the equation is eponential, state the equation. a) y b) y c) y d) y ) The half life of a radioactive substance is one day. This means that, after every day, there is only half of the substance remaining. We will start with g of the substance. Complete the chart and answer the following questions. d a y s Amount (g) First Differences Ratio a) Draw a graph to represent this situation. b) Does this represent eponential growth or decay? c) State the domain and range of this situation. d) Write an equation to represent this situation. e) Use the equation to determine the amount of the substance after one week. f) Use the equation to determine the amount of the substance after one month ( days). g) How long would it take the substance to reach approimately g? Use guess and check.

4 8) Given the following eponential equations: a) State the y-intercept. b) State the common ratio. c) State whether it is increasing or decreasing. d) State the domain and range. i) y = 8() ii) y =.(.) iii) (.) iv) () 9) Evaluate the following epressions: a) b) c) - d) e) f) ) Simplify the following epressions. Write your answers as positive eponents. a) ( )( 7 ) b) ( ) e) ( y) ( y ) 7y c) 8 8 f) ( 8a b ) g) a b a b d) ( y) h) ( y) ( y) ( 8 y ) ) Tommy bought a Wayne Gretzky card years ago for $8. Every year it appreciated in value by 8%. a) Based on the information above, write an eponential equation to represent the value, V of the card after n years. b) What is the domain and range for this function? c) Use the equation to determine the card s value today. ) Jen bought a car for $. The car s value depreciates at a rate of % per year. a) Eplain how this situation represents an eponential function. b) Determine the equation of this eponential function where V is the value of the car and n is the number of years. c) What is the domain and range for this function? d) Use the equation to determine the value of the car after years. ) Terry invests $ into an account that pays.%/a compounded semi-annually. How much will Terry have in the account after years? Assume that he makes no deposits or withdrawals. How much interest did he collect? ) How much does Tracy need to put into an account now that pays 8%/a compounded quarterly so that she will have $ in years? ) Rob invests $, so that he can afford his tuition in years from now. If he gets 7% interest, compounded semi-annually, how much will he have in years? ) Holly puts $ away in an account that pays.% interest, compounded quarterly. How long will it take for it to be worth $? 7) Igor wants to visit Scotland in years. The trip will cost him $. How much must he put in an account now if it pays 9.%/a compounded monthly so that he will have enough money in years? Questions #8 - # must be done on a Graphing Calculator 8) Jake deposits $8 every month into an account that pays.%/a compounded semi-annually. How much will Jake have in years? How much interest will he make? 9) Yin is making quarterly deposits of $ in an attempt to save enough money for a new house in years. What interest rate, compounded quarterly, would her account have to pay so that she will have $ in years? ) Samantha wants to buy a motorcycle. She can borrow $ at %/a compounded quarterly, and repay the loan with equal quarterly payments for si years. Find the quarterly payments that Samantha must make?

5 ) Fleur buys a new car for $ down and pays $ at the end of each month for 7 years. If the finance charge is 9.%/a compounded monthly, a) What is the selling price of the car? b) How much interest will Fleur pay in total for the car? TRIGONOMETRY ) Given the following triangles, find the value of. Note: Diagrams are not drawn to scale. a) b) c) d) 7 m m cm 98. cm cm cm 8 cm 7 ) For the following triangle. Find the value of all missing sides and angles. cm 7 cm cm ) To calculate the height of a tree, Marie measures the angle of elevation from a point A to be. She measures her distance to be 8 m from the base of the tree. How high is the tree to the nearest tenth of a metre? ) A building. m tall casts a shadow of. m along the level ground. At what angle do the rays of the sun hit the ground (to the nearest degree)? ) Two airplanes leave an airport. Plane A leaves at a heading of N7 W and Plane B leaves at a heading of S8 W. An hour later, Plane A has traveled km while Plane B has traveled km. How far apart are the planes at this time? 7) A microwave relay tower. m high is placed on top of a building, as shown in the diagram. From point A, the angles of elevation to the top and bottom of the tower are measured as 8. and. respectively. Find the height of the building. Tower A Building 8) A greenhouse is. m wide. One side of the roof makes an angle of with the horizontal while the other side makes an angle of 7 with the horizontal. Find the length of the longer rafter.

6 PERIODIC FUNCTIONS 9) The graph below shows the vertical displacement of a weight attached to the end of a spring over time. a) State the maimum and minimum Weight on a Spring height of the weight. b) What is the period of this function? What does the period mean? c) What is the amplitude of the curve? 8 How does this relate to the spring? d) Determine the equation of the ais of the curve. e) State an appropriate domain and 8 8 range to represent this situation. Height Above Floor (mm) Time (s) ) Graph the following sinusoidal functions. y = sin( - ) b) y = -sin() c) y = sin() + d) y =.sin( + ) - ) Write the sinusoidal functions that represent the following graphs. a) The amplitude is and the ais of the curve is at y = -. c) b) The amplitude is. and the phase shift is to the left. y ) The depth of water, d(t) metres, in a seaport can me approimated by the sine function d(t) =.sin(.t.77) +., where t is the time in hours. a) Using the TI-8, graph the function for t. Note: for this to work your calculator must be set to RADIANS. b) What is the maimum and minimum displacement of the waves? c) What is the equation for the ais of the curve? What does this mean? d) What is the amplitude of the waves? e) Find the period to the nearest tenth of an hour. f) A cruise ship needs a depth of a t least m of water to dock safely. For how many hours in each period can the ship dock safely? Round answers to the nearest tenth of an hour. ) This data was collected on the east cost of Canada on August th and relates the height, h, of a tide to the time of day, t. The time is measured using the hour clock. t h a) Graph this data using the TI-8 calculator and find the equation for the curve of best fit. b) How high is high tide and how low is low tide? c) Determine the amplitude, period and ais of the curve for this function. Eplain what each of them mean with respect to this situation. d) Determine the height of the tide at :am and at : pm on the same day.

7 ANSWERS.a) Not a function D={-,,7} R= {,} b) Function D={-,-,7,8,} R = {-,,,} c) Not a function D={-,,,7} R= {,,,,8} d) Function D={ εr} R= {y yεr} e) Not a function D={ -,εr} R={y - y,yεr} f) Funciton D={ εr} R= {y y,yεr}. a) 7 b) - c) d).a) Verte (,9.) b) Yint (,8) c) Zero (7,) d) m e) D is time for the time D={ 8,εR} R is heights possible R={y - y 9.,yεR} f) VF y=-.8( - )² + 9. SF y=-.8² FF y=-.8( 7)( + ). b) Verte (7,8) c) Zeroes (.,) and (8.8,) d) D={ εi} R= {P P 8,PεR}. a) Zeroes (,) and (-,) Verte at (-,-9) b) Zeroes (,) and (7,) Verte at (,8) c) Zeroes (-7,) and (-,) Verte at (-,-.). a) ² - 8 b) ² - c) ² d) ³ - ² a) (a² + ) b) (k + )(k + ) c) (b + 9)(b 9) d) ( )( + ) e)( + )( ) f) ( + )( ) g)( 9)( 8) h)( 8)( + ) 8. a) = and = b) =- and =. c) = - 7 and = - 9. a) y=( )( ), Verte (.,.), Min b) y=( 9)( + ), Verte (., -.), Min c) h = (t² + ) no zeroes (doesn t factor), h = (t )² + Verte (.), Min. y= -¼( + )( 7). a) y= ( + )² +, Verte (-,) Min b) y= -( )² + 9, Verte (,9) Ma c) y =.( + 8)² -, Verte (-8,-), Min. a) zeroes b) zero c) zeroes. a) 8.9m b). seconds c) D= {t t.,tεr} R={h h 8.9,hεR}. a) 7m b) m c) s d). s e) D= {t t.,tεr} R={h h,hεr}. a) Quad y=-.8² b) D={ εr} R={y y 9,yεR} (other interp.) c) =-.7 and =.87 d) 9 e) 87% f).8 and.

8 . a) Linear, D={ εr} R={y yεr} b) Ep, D={ εr} R={y y>,yεr} y=.() c) Quad, D={ εr} R={y y yεr} d) Ep, D={ εr} R={y y>,yεr} y=.() 7. b) Decay c) D={ >,εr} R={y y>,y,yεr} d) y=(.) e). - f) 8. i ii iii iv Yint (,8) (,.) (,) (,) Ratio.. Incr/decr Inc Dec Dec Inc Domain D={ εr} D={ εr} D={ εr} D={ εr} Range R={y y>,yεr} R={y y>,yεr} R={y y>,yεr} R={y y>,yεr} 9. a) b) c) /9 d) e) 7 f) /78. a) b) c) 8 d) y e) y a f) ab g) 9 b 8 h) 9 y. a) V = 8(.8) n b) D = {n n,nεr} R = {V V 8,VεR} c) $.99. a) Constant ratio b) V = (.88) n c) D = {n n,nεr} R = {V V,V,VεR} d) $.. $.7. $. to : (Bold is what was solved for) N 8 I% PV PMT FV.8 7. P/Y C/Y PMT: END END END END END END END continued: a) $8.8 b) Interest = $8.. a) b).87m c) d). 7,,..m...8km 7..m 8..9m 9. a) Ma, min b) Period 8s c) d) y = e) D={,εR} R={y - y,yεr}. a) y=sin b) y =.sin( + ) c) y=sin( + ). b) Ma.9, Min.9 c) y =. d). e) hours f) 8. hours. b) Ma 7., Min.8 c) Ais y = 7., Amp., Period hours d) 7. and.9