IF.4.AIII.6
Build functions to model real-world applications using algebraic operations on functions and composition of functions, with and without appropriate technology [e.g., profit functions as well as volume and surface area (optimization subject to constraints)]
Example Problems
Mateo operates a greenhouse during the winter.
The electricity used, E, in kilowatt‑hours, to heat the greenhouse for h hours is .
The cost, C, in dollars, of using q kilowatt‑hours is .
Write an expression that models the cost of heating the greenhouse for h hours.
The electricity used, E, in kilowatt‑hours, to heat the greenhouse for h hours is .
The cost, C, in dollars, of using q kilowatt‑hours is .
Write an expression that models the cost of heating the greenhouse for h hours.
Bryce owns a vineyard in the foothills.
The liters of grape juice, G, obtained from b baskets of grapes is .
The number of wine bottles, B, that can be filled from l liters of juice is .
Write an expression that represents the number of wine bottles produced as a function of the number of baskets of grapes harvested.
The liters of grape juice, G, obtained from b baskets of grapes is .
The number of wine bottles, B, that can be filled from l liters of juice is .
Write an expression that represents the number of wine bottles produced as a function of the number of baskets of grapes harvested.
Zara operates a mobile car‑wash service.
The number of cars washed, W, during d hours on the road is .
The income, I, in dollars, from washing n cars is .
Write an expression that represents Zara's income as a function of the number of hours spent on the road.
The number of cars washed, W, during d hours on the road is .
The income, I, in dollars, from washing n cars is .
Write an expression that represents Zara's income as a function of the number of hours spent on the road.
Khan Academy ResourcesComposing functionsIntro to composing functionsFind composite functionsModel with function combinationEvaluate composite functionsModel with composite functionsEvaluate composite functions: graphs & tablesEvaluating composite functionsModeling with composite functionsEvaluating composite functions: using tablesIntro to composing functionsMeaningfully composing functionsEvaluating composite functions: using graphsModeling with composite functions: skydivingModeling with function combinationFinding composite functionsFunction notation word problem: bankEvaluating composite functions (advanced)
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