Stewart6e1_2

# Stewart6e1_2 - MATH 191, Sections 1 and 3 Calculus I Fall...

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MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 1.2: Modeling with Functions In our last class we saw some examples of mathematical , functions which closely describe the behavior of “real-world” quantities or phenomena. What sorts of functions, and therefore models, are there? Let’s look at some examples: 1. One of the functions from last class was T ( p ), the temperature at which water boils as a function of pressure p . Physics tells us that there is a relationship between T and p , and therefore the graph of T is a , something like: 2. Slightly more generally, functions of the form f ( x ) = a 0 + a 1 x + ··· + a n x n (for some non-negative integer n for which a n 6 = 0) are called . The numbers a i ( i = 0 ,...,n ) are called the of f , and the number n is called the of f . If f has degree 2, 3, or 4, it is called quadratic , , or quartic , respectively. You should be able to plot each of these general shapes below:

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3. Power functions have the form f ( x ) = x a for some not-necessarily integer
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## This note was uploaded on 04/08/2008 for the course MATH 191 taught by Professor Bahls during the Fall '07 term at UNC Asheville.

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Stewart6e1_2 - MATH 191, Sections 1 and 3 Calculus I Fall...

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