c)How does the volume function in part a)change if the height of the box is doubled?tripled? Describe the family of functionsformed by multiplying the height by a constant.x123123412182430364260yx123123412182448 cmxxxx60 cmd)Sketch graphs of two members of thisfamily on the same coordinate grid.19.The graph represents a section of the trackof a rollercoaster. Write an equation for thefamily of functions that models the section ofthe track.yx123123412182430364260yx123123412182448 cmxxxx60 cm6612180

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2.4 Families of Polynomial Functions • MHR121

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20.An open-top box is to be constructed from apiece of cardboard by cutting congruent squaresfrom the corners and then folding up the sides.The dimensions of the cardboard are shown.The design for the crystal pieces of thechandelier at the beginning of this sectionis shown below. Determine an equationfor the family of functions used to createthe design.b)Find equations for the members of thefamily that make up the design.c)Create a design of your own. Write equationsfor the family of functions and the membersused in your design.xxa)Express the volumeof the box as afunction ofx.b)Write an equationto represent a boxwith volume that isi)twice the volume of the box representedby the function in part a)ii)three times the volume of the boxrepresented by the function in part a)c)How are the equations in part b) related tothe one in part a)?d)Sketch graphs of all three functions on thesame coordinate grid.e)Determine possible dimensions of a boxwith volume 1820 cm3.✓Achievement Check21. a)The design for the crystal pieces of thechandelier at the beginning of this sectionis shown below. Determine an equationfor the family of functions used to createthe design.b)Find equations for the members of thefamily that make up the design.c)Create a design of your own. Write equationsfor the family of functions and the membersused in your design.xxyx123451239060120150303060901201500CExtend and Challenge22. a)Write an equation for a family of evenfunctions with fourx-intercepts, two ofwhich are2_3and 5.b)What is the least degree this family offunctions can have?c)Determine an equation for the member ofthis family that passes through the point(1,96).d)Determine an equation for the member ofthis family that is a reflection in thex-axisof the function in part c).23.Refer to question 19. Design your ownrollercoaster track using a polynomial functionof degree six or higher. Sketch a graph of yourrollercoaster.24.Math ContestTwo concentric circles haveradii 9 cm and 15 cm. Determine the length ofa chord of the larger circle that is tangent tothe smaller circle.25.Math ContestGiven a functiong(x) such thatg(x22)x45x23, determineg(x21).24 cmxx36 cmConnectingProblem SolvingReasoning and ProvingReflectingSelecting ToolsRepresentingCommunicating122MHR • Advanced Functions • Chapter 2

Solve InequalitiesUsing Technology2.5An electronics manufacturer determines that the revenue,Rin millions of dollars, from yearly sales of MP3 players can bemodelled by the functionR(t)t30.8t22t1, wheretthe time, in years, since 2003. How can this model be used todetermine when the yearly sales will be $100 million or more,that is, when willt30.8t22t1100?,is

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WOCK

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