1.4 Combination of Functions.pptx - CALCULUS 12 1.4...

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Unformatted text preview: CALCULUS 12 10/29/19 1.4 Combination of Functions Do you remember what means? Lesson Objective By the end of the lesson, I will be able to… Perform operations on functions and to evaluate composition of functions Review knowledge from Pre-Calc 12 Ex1. Adding, Subtracting, Multiplying Functions Given: Graph: a) and b) c) d) Hint: Use a table of values Composition of Functions (Composite Functions) When you apply two functions in succession, the resulting function is called a ‘composition of two given functions’ Ex2. Practice Ex 3. Ex 4. Given and a) b) Practice Ex5. Given the table… a) b) c) x f(x) g(x) -2 1 -4 -1 0 -1 0 -1 2 1 -2 5 2 -3 8 f(x) Practice Ex6. Given the graphs… a) b) c) g(x) Ex 7. A square has side length of x. a) Write a function for the square area, A, in terms of x. b) Write a function for the side length x in terms of the perimeter, p. c) Determine A(x(p)). d) A cardboard`s perimeter is 6 cm. What is the area of the cardboard? x x Ex8. Business Application Sam buys a box of oranges and has a coupon for $2 off. The day he buys the box of oranges, the store has a sale offering 10% off the price of all fruits. a) Write a function to represent the cost, , of a box of oranges at price , if just the coupon deduction is applied to the cost of the box of oranges. Write a function that represents the cost, , if just the discount is applied to the cost of oranges at price Ex8. Business Application b) What does the function D(C(p)) represent if a box of oranges? “D(C(p)) represents…. “ c) What does the function C◦D represent? “In real life, C◦D happens would be when…” Ex8. Business Application d) If a box of oranges regularly costs $24, would you prefer D(C(p)) or C◦D? Why? “I prefer ____ because …” “If a box of oranges is $24, then would…” “I think that _____ is the better choice because …” Lesson Objective By the end of the lesson, I will be able to… Perform operations on functions and to evaluate composition of functions Review knowledge from Pre-Calc 12 Suggested Practice Page 111 Exploration Problem Page 112 #13-27,37-49,57,59,67,69. (Do only odd-numbered questions.) Vocabulary: Composition of functions ...
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