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PP Section 4.4 - DefineFunctions Comments...

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Setting Up Equations that  Define Functions
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Comments   This is the first step in modeling in mathematics.     Modeling means replacing the words of  whatever language is being used by  mathematical expressions.   Solving an application problem has as first step  modeling the problem.
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Steps to Follow 1. Read the problem carefully and draw diagrams, if  appropriate. 2.  Assign variables to key quantities. 1. Label the diagram and any other  quantities relevant to the problem. 4.  Write the equation(s) relating the quantities  above.
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Example The length of the rectangle is twice its width.   Write the perimeter and the area of the rectangle  as functions of its width. w = width 2w       P(w) = 2w + 2(2w)= 6w   A(w) = w(2w) 2 2w = w
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Example Let  2s  denote the length of the side of an equilateral  triangle.  Find a formula for the area of the triangle as a 
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