You must completeTone from each row and each column. Exponential Function Polynomial Function Trigonometric Function Graphical & Numeric Given: The graph below Givenc Given: Graph below Models Function #1 Function #2 Numeric model Graphical Model Knowledge/Understanding -11 -1 1. State: domain and range -18 x and y intercepts if applicable 1. State: max and min if applicable domain and range relative max and min if applicable, X and y intercepts end behaviour if applicable 1. For each model above, state: max and min values and where they occur whether it models growth or decay domain and range period Initial amount x and y intercepts if applicable amplitude asymptote max and min if applicable ands of symmetry 2. Determine f(3] relative max and min if applicable values of a, k, d, and o for the sine function 3. Determine the value of x if fix) = 1 end behaviour if applicable 2 Describe how this graph is related to the base function yesin x by Graph the log function related to this type oil polynomial function with proof referring to horizontal and vertical shifts, amplitude, compressions or function. degree of each expansions, reflection. 2. Determine f(-2) for each model. 3. Determine the value of x if fix = -8 for graphical modet solve fix) = 8 for numeric model. Algebraic Model Task Task Task : 1. Create an algebraic model with these Given these key features Create an accurate algebraic model using both sine and cosine given parameters: these parameters: Application one for decay - clearly define explain leading coefficient is -2 "vertical shift up 5 units from base function fix) = sinx and g(x] = decay factor zeroes 21 -3, -1, 4 one for growth of 35%% Domain: 45 5 x 5 675 5x5675 y intercept of 10 Create two possible algebraic models, using two different degrees of polynomial functions. 4 cycles within domain 2. For both functions, determine fio), -5), and Express both in standard and factored form. horizontal shift 45 left solve fix) = 32 using logarithms. Show one example proving: fla) . .[[b) = ta + vertical stretch by a factor of 3 3. State the range of the function. bj using rational exponents. [.e. (b 6 16 6 Determine NO), f( 180 ] and solve fix) = b, for all x within domain, where b is the maximum. Real-World Application 1. Describe two different situations that could be Collect some real-world data from two of the sources listed below. 1. On the Intemet find two applications for trigonometric functions. modelled by an exponential function. Show which type of polynomial function best fits the data and give reasons. (must be Cannot be Ferris Wheel ride or tides or hours of daylight. Clearly define all variables in the relationship two different types of polynomial functions) Clearly define variables in the relationship. 2. Cite your sources and explain why this model is a good fit by referring 3 Thinking/Communication Interpret the growth or decay factor and the Be specific with your reasoning by relating to key features of the polynomial function. to key features of this function that relate well to the application. Initial amount, which cannot be 1. Your justification should also include reference to at least two of graphical, numeric, 3. Clearly define variables in the relationship. 4 Explain why this type of function makes sense andfor algebraic models. Your justification should also include reference to at least two of as a model for these real applications, by Transportation Energy Data Book - vehide energy efficiency. graphical, numeric, and'or algebraic models. referring to key features of this function. NationMaster - a compilation of data from sources such as: CIA World Factbook, United Nations, Your justification should also Include reference World Health Organization, World Bank, World Resources Institute, UNESCO, UNICEF, OECD. to at least two of graphical, numeric, and/or The Numbers - Box office data, movie stars. algebraic models. Quantrafive Environmental Learning Project -Supported by the National Science Foundation. WWodd Climateand Temperature indexmund - detailed country statistics, charts, and maps compiled from multiple sources. Healthy Youth Nutrition Facts Health in Canada - resource for Canadian health statistics. NHL stats Census at School - data on multiple topics of school-aged children Economic - Economic Time Series Data