will use your knowledge ofadvanced functionsand the graphing calculator desmos to create an animated design that is inspired byyour hobbies. You will also analyze some of the functions used in your design andcomplete a summary table.

Desmos Animated Design =3) X + Rational Functions X 80 Exponential Functions X 60 D Logarithmic Functions X Trigonometric Functions X 40 Sum or Difference Functions X 20 Product Functions X Quotient Functions X -80 60 -40 -20 0 20 40 60 Composite Functions X -20 Summary Table Functions XSummary Table 1 - Choose functions from your desmos animated 3 - Justify your work using equations, theorems, graphs design to complete the summary table below. in order to get full marks. 2 - Fully answer the question asked for each function in 4 - Submit your completed summary table in the the table. culminating project folder in Brightspace. 1 A sum or difference of two State the Local Max and Local Min. Justify your answer with reference to the y 3. A quotient of two functions State the Domain, Range and vertical or horizontal Asymptotes. Justify young y functions with at least one graph of this function and the sign of IRC. Provide a sketch of your function. answer with reference to your equation and graph. Provide a sketch of your max or min function. Function from your design Function from your design Disregard desmos restrictions. Set sliders to 0 or 1 if needed Disregard desmos restrictions. Set sliders to O or 1 if needed Very Important Note: f(x) = + 5 cannot be used as 2. A product of two functions Determine the x Intercepts and y intercept. Justify your answer with it is not a quotient. Ax) = with at least one x intercept calculations and show algebraic steps to determine the x intercepts and the y intercept. can be used in the summary table Function from your design 4. A composite function Determine the Instantaneous Rate of Change at x=A Choose a value for A in the domain of your function and show full calculations. Disregard desmos restrictions. Is the function increasing at that point? How do you know? Set sliders to 0 or 1 if needed Function from your design Very Important Note: Disregard desmos restrictions. ((x) = mix. dogx - 4 cannot Set sliders to O or 1 if needed be used as it is not a quotient. fox) = sox . dog x can be used In the summary table1. A sum or difference of two functions with at least one man: or min Function from your design Disregard desmos restrictions. Set sliders to n or 1 if needed 2. A product of two functions with at least one x intercept Function from your design Disregard desmos restrictions. Set sliders to [i or 1 if needed Vervlmporbsnt Note: HI] = sin XI Iogx 4 cannot be used as it is not a product. {(1) = sin 1- logx can he used in the summary table State the Local Max and Local Min. Justify 1.rour answer with reference to the graph of this function and the sign of IRE. Provide a sketch of your function. Determine the ac intercepts and 1r intercept. Justify your answer with calculations and show algebraic steps to determine the x intercepts and the y intercept. 3. A quotient of two functions State the Domain, Range and vertical or horizontal Asymptotes. Justify your answer with reference to your equation and graph. Provide a sketch of your function. Function from your design Disregard desmos restrictions. Set sliders to 0 or 1 if needed Very Important Note: f(x) = logx sinx + 5 cannot be used as it is not a quotient. A(x) = logx sinx can be used in the summary table 4. A composite function Determine the Instantaneous Rate of Change at x=A Choose a value for A in the domain of your function and show full calculations. Is the function increasing at that point? How do you know? Function from your design Disregard desmos restrictions. Set sliders to 0 or 1 if neededThe animated design must meet the following criteria: El It is unique and your own work D D It must have a minimum of 10 functions It includes at least one of each of the functions below: A. B. C. D. E F. Polynomial function {degree 3 or higher) Exponential function Logarithmic function Trigonometric function . Rational function A sum or difference function with at least one local maximum or minimum. The two functions added must be from two different categories A, E, C. D. E fag. a trig 8. a rational} . A product function with at least one x intercept. The two functions multiplied must be from two different categories A. B. G, D, E {eg. a trig St a rational) . A quotient function. The two functions that are divided must be from two different categories A, E, C. D. E (eg. a trig s a rational} A composite function. The inner and outer function must be from two different categories from the categories above A. El. '3. D, E {eg. trig St a rational) No other functions allowed. This means no linear, quadratic, absolute value functions allowed or functions that were not covered in this course. You must not use functions that simplify linear or quadratic functions