Graphing Piecewise FunctionsDate: 09/09/2001 at 23:19:36 From: Mary Subject: Piecewise Functions (Algebra II) I do not understand how to GRAPH piecewise functions. Graph: {2x if 0<_ [that's less than or equal to] x<2} f(x)={4 if 2<x<4} {-1/4x +5 if 4<_ x<_6} I know it is hard to understand what I wrote, but please help me! Thank you so much. Mary Date: 09/10/2001 at 08:51:30 From: Doctor Peterson Subject: Re: Piecewise Functions (Algebra II) Hi, Mary. You have the function defined in three parts; you can start by marking the domains of those parts on the graph, by drawing (lightly) the vertical lines x = 0, x = 2, x = 4, and x = 6. Now, again lightly, draw the lines y = 2x y = 4 y = -1/4 x + 5 Finally, you have to cut out the pieces that form the given function and glue them together (figuratively). Look in the region 0 <= x < 2, and darken the first line only within that region, that is, between the lines x = 0 and x = 2. Then, in the region 2 < x < 4, darken the second line, and in 4 <= x <= 6, darken the third line. The darkened portions consitute the function f(x), which is therefore defined only on the domain 0 <= x <= 6. In this case, you will find that the three segments actually are "glued" together; they meet at x = 2 and x = 4. That isn't always true, but when it is it can help you feel confident. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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