can you please help me with this it's grade 11 mathematics can you please help me with the last part Trigonometric Function.

Exponential Function Polynomial Function Trigonometric Function Graphical & Numeric Given: The graph below Given: Given: Graph below Models Function #1 Function #2 Numeric model Graphical Model X f(x) 64 Knowledge/Understanding -42 -3 -24 - 2 OT- -1 -10 -8 -2 2 1. State: o a) domain and range -10 O b) x and y intercepts if applicable 1. State: o c) max and min if applicable d) relative max and min if domain and range applicable, x and y intercepts O e) end behaviour if applicable 1. For each model above, state: . max and min values and where they occur o f) whether it models growth or a) domain and range . period decay b) x and y intercepts if applicable amplitude O Initial amount c) max and min if applicable axis of symmetry o asymptote d) relative max and r values of a, k, d, and c for the sine function equation. 2. Determine f(3 e) end behaviour if applicable 2. Describe how this graph is related to the base function y=sin x by 3 termine the value of x if f(x) = 1 f) type of polynomial function with proof referring to horizontal and vertical shifts, amplitude, compressions or . g) degree of each expansions, reflection. 2. Determine f(-2) for each model. 3 . Determine the value of x if f(x) = -8 for graphical model; solve f(x) = 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: f(0) = 5 these parameters: Application one for decay - clearly define/explain vertical shift up 5 units from base function f(x) = sinx and g(x) = decay factor zeroes at -3, -1, 4 OS X. . one for growth of 35% Domain: -45 S x S 675 y intercept of 10 What is the leading coefficient? 4 cycles within domain For both functions, determine f(0), f(-5), and horizontal shift 45 lef solve f(x) = 32 using logarithms and explain in Create two possible algebraic models (different degrees) and provide a graph for each, may use tch by a fa context. technology for the graph. State the range of the function. 3. Show one example proving: f(a).f(b) = f(a + b) Determine f(0), f(180 ) and solve f(x) = b, for all x within domain, where b using rational exponents. [i.e. (ba)(bd)=ba+d] 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 Internet find two applications for trigonometric (sinusoidal) modelled by an exponential function, one Show which type of polynomial function best fits the data and give reasons. (must be functions. Cannot be Ferris Wheel ride or tides or hours of daylight. growth and one decay. 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 2. Clearly define all variables in the relationship. 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 Thinking/Communication Interpret the growth or decay factor and the Your justification should also include reference to at least two of graphical, numeric, 3. Clearly define variables in relationship. initial amount, which cannot be 1. and/or algebraic models. 4. Your justification should also include reference to at least two of 4. Explain why this type of function makes sense Transportation Energy Data Book - vehicle energy efficiency. graphical, numeric, and/or algebraic models. as a model for these real applications, by NationMaster - a compilation of data from sources as: CIA World Fact book, United Nations, referring to key features of this function World Health Organization, World Bank, World Resources Institute, UNESCO, UNICEF, OECD. 5. Your justification should also include reference The Numbers - Box office data, movie stars. o at least two of graphical, numeric, and/or Quantitative Environmental Learning Project -Supported by the National Science Foundation. algebraic models. World Climate and Temperature indexmundi - 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 Economagic - Economic Time Series Data