Advanced Functions by Chris Kirkpatrick, Marian Small, Barbara Alldred

By Chris Kirkpatrick, Marian Small, Barbara Alldred

Built for the ON Grade 12 complex services Curriculum MHF4U, Revised 2007. gains & merits include:

• complete, digital model of the coed textual content on CD, in PDF format
• bankruptcy Openers with abilities and inspiration Reviews
• Getting begun, together with assessment of key vocabulary, key techniques, and understandings
• Mid-Chapter and bankruptcy reports 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 fulfillment Chart classification questions pointed out in each lesson
• precis of Key principles and ideas in each lesson
• know-how help contains: TI-83 Plus, TI-84 Plus, The Geometer's Sketchpad®, Spreadsheets, TI-Nspire CAS Handhelds
• unfastened on-line entry to applets and different functional eTools that carry the maths to lifestyles

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58 Chapter Review NEL Chapter Review Q: Is an inverse of a function always a function? A: No; if an element in the domain of the original function corresponds to more than one number in the range, then the inverse relation is not a function. 5, Examples 1, 2, and 3. • Try Chapter Review Questions 10 to 13. Q: What is a piecewise function? A: A piecewise function is a function that has two or more function rules for different parts of its domain. 6, Examples 1, 2, 3, and 4. Questions 14 to 17. consists of two pieces.

State the domain and the range of the function. 2x, if x , 1 f (x) 5 e x 1 1, if x $ 1 15. Write the algebraic representation for the following piecewise function, using function notation. 6 4 x 1 2 3 4 5 –4 –6 x 2 1 1, if x , 1 3x, if x $ 1 is f (x) continuous at x 5 1? Explain. NEL 18. Given f 5 5(0, 6), (1, 3), (4, 7), (5, 8)6 and g 5 5(21, 2), (1, 4), (2, 3), (4, 8), (8, 9)6 , determine the following. a) f (x) 1 g(x) b) f (x) 2 g(x) c) 3 f (x)43 g(x)4 19. Given f (x) 5 2x 2 2 2x, 22 # x # 3 and g(x) 5 24x, 23 # x # 5, graph the following.

B) State the domain and range. 5 4 2. Given the following information about a function: 3 2 1 –5 –4 –3 –2 –1 x 0 D 5 5xPR6 R 5 5 yPR 0 y $ 226 decreasing on the interval (2 `, 0) increasing on the interval (0, ` ) a) What is a possible parent function? b) Draw a possible graph of the function. c) Describe the transformation that was performed. • • • • 3. Show algebraically that the function f (x) 5 0 3x 0 1 x 2 is an even function. 4. Both f (x) 5 x 2 and g(x) 5 2x have a domain of all real numbers.

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