advertisement

PreCalculus 11 Chapter 7/8 Project Name______________________ Paint – by – Functions *This project is NOT optional – it takes the place of your chapter test and will be worth approximately 50% of the chapter’s mark. Your mission: create a pretty picture composed of functions. Your picture must include: 1 linear functions 1 quadratic functions 1 “linear” absolute value function 1 “quadratic” absolute value function 2 reciprocal functions (the original versions do not have to be shown) the absolute value or reciprocal function of any general “f(x)” functions that are drawn but not described by equations (to allow you to draw whatever shapes you need 1 linear-quadratic or quadratic-quadratic system. Your description should include intersection points, graphically highlighted and verified algebraically. - You’ll hand in: a) Your lovely picture. Flattering portraits of your math teacher may get extra credit. b) A page of functions, with domain/range statements matching the criteria above, that created your picture. Descriptions: 1a. y 1 ( x 25)2 45 1b. y 1 ( x 25) 2 45 D: 22< x < 27 D: 30 < x < 35 . . 2a. y = 0.22(x-90) 2 + 100 D: 55<x<65 2b y = 0.22(x-94) 2 + 100 D: 65<x<75 . . 3. y = 0.33(x-30) 2 + 80 y = 0.25(x-30) 2 + 70 D: 0<X<60 Intersection points: 0.33(x-30) 2 + 80 = 0.25(x-30) 2 + 70 0.33(x-30) 2 + 10 = 0.25(x-30) 2 0.33x2 + 20x + 300 = 0.25x2+15x+225 …. Intersects: (0,40) and 55,45) Use domain/range statements to limit the extent of the functions on the page, to hide parts of the functions that shouldn’t appear. Use pencil crayons, highlighters, etc. to color the functions and regions of your picture. The origin can be either in the lower-left corner or elsewhere on the page; the page can be oriented landscape or portrait. You can collaborate with a partner, but you must each produce your own project. Hand in the picture, plus the marking guide. Fill in your own marking guide with your most honest assessment of your work. Technology option: using the Desmos online calculator or another digital tool re-create your picture digitally. This option earns 5% in bonus marks. Example: Your functions will be different from these, obviously, to meet the criteria above. Note the domain statements that precede each function. PrintScreen and print your digital version and hand in with your paper version. Marking Guide: 1 Linear Function Absolute Value Functions Major Error (in graphing or domain/range statement) 2 Minor Error (in graphing or domain range statement) 3 No Errors: Initial function represented correctly Function is transformed Domain / Range stated Quadratic Function General function y f ( x) Linear Function Reciprocal Functions Major Error (in graphing or domain/range statement) Minor Error (in graphing or domain range statement) No Errors: Initial function represented correctly Function is transformed Domain / Range stated Major Error in calculation Minor Error in Calculation Used relevant mathematical concepts efficiently Major Error in calculation Minor Error in Calculation Used relevant mathematical concepts efficiently Quadratic Function General function y f ( x) LinearQuadratic Systems QuadraticQuadratic Systems Technology and Visualization Problem Solving Graph is not appropriate or major errors. Student required substantial assistance or missed asking assistance which would have improved their project Constructs appropriate graphs; may contain minor errors Student sought minor, but necessary assistance Constructs appropriate graphs effectively Student independently created functions that represent each shape, checking correctness as necessary