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Mathematical Models Constructing functions

Mathematical Models Constructing functions. Objective: Construct and Analyze functions. Real world problems.

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Mathematical Models Constructing functions

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  1. Mathematical ModelsConstructing functions Objective: Construct and Analyze functions

  2. Real world problems • These problems often result in mathematical models that involve functions. These functions need to be constructed or built based on the information given. In constructing functions, we must be able to translate the verbal description into the language of mathematics. We do this by assigning symbols to represent the independent variable and then finding the function or rule that relates the variables.

  3. EX: Demand equation: the price p and the quality x sold of a certain product obey the demand equation • a) Express the revenue R as a function of x. (Remember, R=xp) • b) What is the revenue if 200 units are sold?

  4. Let be a point on the graph of • a) Express the distance d from P to the origin as a function of x • b) What is d if x=0? c) What is d if x=1?

  5. A rectangle has one corner on the graph of ,another point at the origin, a third on the positive y-axis, and the fourth on the positive x-axis • a) Express the area A of the rectangle as a function of x • What is the domain of A?

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