Functions: Domain, Range, and PiecewiseDate: 08/31/98 at 21:07:29 From: Anonymous Subject: Pre-Calculus Honors What exactly are piecewise functions? What are open and closed points? How do you figure out the domain and range of a function without graphing it on a calculator? Please help. Date: 08/31/98 at 22:18:49 From: Doctor Jaffee Subject: Re: Pre-Calculus Honors Hi there, If you have a function in which x is the independent variable and y is the dependent variable, the domain is the set of all the x numbers. Normally, x can be any number, but if it is inside a radical sign, you need to see whether there are values of x that will make y imaginary. Those x numbers can't be in the domain. If x is in the denominator of a fraction, any value of x that would make the denominator zero must be eliminated. If you can solve the equation for x in terms of y, you can use the same procedure to determine the range. Now, this is not a complete answer, but it addresses the great majority of cases. If you have a function that is determined by one expression for some values of x, and then is determined by another expression for other values of x, then that function is what we call "piecewise." For example, y = x^2 for x < 3 and y = 2x + 1 for x > or = 3. On the curve y = x^2, x can't equal 3, so the end of the curve, (3,9), is open. But on the line y = 2x + 1, x can equal 3, so the end of the line, (3,7), is closed. I hope this explanation clarifies the situation somewhat. If you still have questions, write back and I or one of the other doctors will try to help. Good luck in your course. - Doctor Jaffee, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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