Graphing an EquationDate: 11/08/97 at 22:27:10 From: Perry Loh Subject: Graphing an equation I was wondering if you could explain the following question to me: y = a+b(x)+c(x^2)+... I don't know how to work with this equation or what kind of graph this equation produces. All help would be great. Thanks. Date: 11/09/97 at 09:25:47 From: Doctor Chita Subject: Re: Graphing an equation Hi Perry: This does look mysterious, doesn't it! Actually, the equation is a general one that represents any polynomial function. A polynomial is an expression containing many terms, usually separated by + signs. A function is a special set of ordered pairs (x, y). In this equation, you have two variables, and y is a function of a polynomial in terms of the variable x. x is the independent variable, and y is the dependent variable. The coefficients of x are real numbers, represented as a, b, c, etc. The exponents of x in every term are non-negative integers. The first term in this equation can be written as a*x^0 where x^0 = 1. That's why you don't see an "x" term. The three dots after the third term is called an ellipsis. It means that the polynomial can go on indefinitely as the exponents increase. For example, y = 3 + 2x + 5x^3 - 4 x^5 is a polynomial function. Here, the exponents of x are 0 (implied), 1, 3, and 5. The "visible" coefficients of x are 3, 2, 5, and -4. That is, a = 3, b = 2, c = 0, d = 5, 3 = 0, and f = -4. Once you identify the exponents and coefficients, you can graph the function on a coordinate plane. Here's a graph of this function: The shape of a graph becomes very interesting, depending on the number of terms in the expression and the constants and exponents. If you have a graphing calculator or a computer, try graphing different functions. Change the constants and/or exponents and see how each change affects the corresponding graph. Polynomial functions are very interesting, especially around the origin. That's where most of the "real" action occurs. Check it out. -Doctor Chita, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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