1-6 Function Operations and Composition of Functions Classwork 1. MARCHING BAND Band members form a circle of 4. TRAVEL Two travelers are budgeting money for the radius when the music starts. They march outward same trip. The r first traveler’s budget (in dollars) can as they play. The function = 2.5t gives the radius be represented by = 45x + 350. The second f(t) f(x) of the circle in feet after seconds. Using = for t g(r) traveler’s budget (in dollars) can be represented by the area of the circle, write a composite function that = 60x + 475, is the number of nights. g(x) x gives the area of the circle after seconds. Then find t the area, to the nearest tenth, after 4 seconds. Find (f + and the relevant domain. a. g)(x) b. What does the composite function in part a represent? 2. CANDLES A hobbyist makes and sells candles at a local market. The function = 4h gives the number c. Find (f + and explain what the value c(h) g)(7) of candles she has made after hours. The function represents. h = 12 + 0.25c gives the cost of making candles. f(c) c a. Write the composite function that gives the cost of d. Repeat parts a–c for (g f)(x). – candle making after hours. h . 3. Find for 5. Find State the domain of each new function. = = =
1-6 Function Operations and Composition of Functions Classwork 1. MARCHING BAND Band members form a circle of radius r when the music starts. They march outward as they play. The function f(t) = 2.5t gives the radius of the circle in feet after t seconds. Using g(r) = for the area of the circle, write a composite function that gives the area of the circle after t seconds. Then find the area, to the nearest tenth, after 4 seconds. 2. CANDLES A hobbyist makes and sells candles at a local market. The function c(h) = 4h gives the number of candles she has made after h hours. The function f(c) = 12 + 0.25c gives the cost of making c candles. a. Write the composite function that gives the cost of candle making after h hours. . 3. Find for = = = 4. TRAVEL Two travelers are budgeting money for the same trip. The first traveler’s budget (in dollars) can be represented by f(x) = 45x + 350. The second traveler’s budget (in dollars) can be represented by g(x) = 60x + 475, x is the number of nights. a. Find (f + g)(x) and the relevant domain. b. What does the composite function in part a represent? c. Find (f + g)(7) and explain what the value represents. d. Repeat parts a–c for (g – f)(x). 5. Find State the domain of each new function.
Pre-Cal_1-6_Function_Operations_and_Composition_of_Functions_Classwork.docx