By Chris Kirkpatrick, Marian Small, Barbara Alldred
Built for the ON Grade 12 complicated capabilities Curriculum MHF4U, Revised 2007. gains & merits include:
• complete, digital model of the scholar textual content on CD, in PDF format
• bankruptcy Openers with talents and notion Reviews
• Getting all started, together with evaluate of key vocabulary, key techniques, and understandings
• Mid-Chapter and bankruptcy studies with commonly asked Questions
• a number of solved examples with causes combine the mathematical process
• wide selection of perform questions steadily expanding in difficulty
• pattern success Chart class questions pointed out in each lesson
• precis of Key principles 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 convey the maths to existence
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A) The formula A 5 pr 2 is convenient for calculating the area of a circle when the radius is known. Find the inverse of the relation, and describe what it can be used for. b) Use the equation given in part a) to calculate the area of a circle with a radius of 5 cm. ) Use the inverse relation to calculate the radius of the circle with the area you calculated. 9. If f (x) 5 kx 3 2 1 and f 21 (15) 5 2, find k. T 10. 5 11. Suppose that the variable a represents a particular student and f (a) represents the student’s overall average in all their subjects.
You may limit the domain to xP [0, 50). Why do you think graphs like this one are often referred to as step functions? 14. Explain why there is no value of k that will make the following function continuous. 5x, if x , 21 f (x) 5 • x 1 k, if 21 # x # 3 2x 2, if x . 3 15. The greatest integer function is a step function that is written as f (x) 5 3x4, where f (x) is the greatest integer less than or equal to x. In other words, the greatest integer function rounds any number down to the nearest integer.
4 –3 –2 –1 0 1 2 3 4 60 Chapter Review 9. (2, 1) is a point on the graph of y 5 f (x). Find the corresponding point on the graph of each of the following functions. 5 17. A telephone company charges $30 a month and 10. For each point on a function, state the corresponding point on the inverse relation. a) (1, 2) d) f (5) 5 7 b) (21, 29) e) g(0) 5 23 c) (0, 7) f ) h(1) 5 10 11. Given the domain and range of a function, state the domain and range of the inverse relation. a) D 5 5xPR6, R 5 5 yPR 0 22 , y , 26 b) D 5 5xPR 0 x $ 76, R 5 5 yPR 0 y , 126 12.
Advanced Functions by Chris Kirkpatrick, Marian Small, Barbara Alldred