By Chris Kirkpatrick, Marian Small, Barbara Alldred
Built for the ON Grade 12 complex capabilities Curriculum MHF4U, Revised 2007. positive aspects & merits include:
• complete, digital model of the coed textual content on CD, in PDF format
• bankruptcy Openers with abilities and suggestion Reviews
• Getting begun, together with assessment of key vocabulary, key innovations, and understandings
• Mid-Chapter and bankruptcy studies with commonly asked Questions
• a number of solved examples with factors combine the mathematical process
• wide array of perform questions steadily expanding in difficulty
• pattern success Chart class questions pointed out in each lesson
• precis of Key rules and ideas in each lesson
• know-how aid contains: TI-83 Plus, TI-84 Plus, The Geometer's Sketchpad®, Spreadsheets, TI-Nspire CAS Handhelds
• loose on-line entry to applets and different functional eTools that carry the mathematics to lifestyles
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Additional resources for Advanced Functions
B. What does h(x) 5 f (x) 1 g(x) represent? 7 C. Simplify h(x) 5 (3x 1 10) 1 (25x 1 200). D. Make a table of values for the function in part C, with the temperature in intervals of 5°, from 0° to 40°. How do the values compare with the values in each table you made in part A? How do the domains of f (x), g(x), and h(x) compare? E. What does h(x) 5 f (x) 2 g(x) represent? F. Simplify h(x) 5 (3x 1 10) 2 (25x 1 200). G. Make a table of values for the function in part F, with the temperature in intervals of 5°, from 0° to 40°.
E) What is the domain of h(x)? How does this domain compare with the domains of f (x) and g(x)? 8. Let f (x) 5 x 2 1 2 and g(x) 5 x 2 2 2, xPR. a) Sketch each graph on the same set of axes. b) Make a table of values for 23 # x # 3, and determine the corresponding values of h(x) 5 f (x) 3 g(x). c) Use the table to sketch h(x) on the same axes. Describe the shape of the graph. d) Determine the algebraic model for h(x) . What is its degree? e) What is the domain of h(x)? NEL Chapter 1 57 1 Chapter Review FREQUENTLY ASKED Questions Study Aid Q: In what order are transformations performed on a function?
In this equation, a 5 3 and c 5 22. 1. a vertical stretch by a factor of 3 2. a vertical translation 2 units down NEL Chapter 1 31 (x, y) S (x, 3y) Parent Function y 5 "x Stretched Function y 5 3"x (0, 0) (0, 3(0)) 5 (0, 0) (1, 1) (1, 3(1)) 5 (1, 3) (4, 2) (4, 3(2)) 5 (4, 6) (9, 3) (9, 3(3)) 5 (9, 9) Vertically stretching the graph by a factor of 3 occurs when all the y-coordinates on the graph of the parent function are multiplied by 3. (x, 3y) S (x, 3y 2 2) Stretched Function y 5 3"x Final Transformed Function y 5 3"x 2 2 (0, 0) (0, 0 2 2) 5 (0, 22) (1, 3) (1, 3 2 2) 5 (1, 1) (4, 6) (4, 6 2 2) 5 (4, 4) (9, 9) (9, 9 2 2) 5 (9, 7) 10 Translating the graph 2 units down occurs when 2 is subtracted from all the y-coordinates on the graph of the stretched function.