Also note that as shown we can put the minus sign on

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Unformatted text preview: nother turning point (at some unknown point) so that the graph can get back up to the x-axis for the next x-intercept at x = 3 . This is the final x-intercept and since the graph is increasing at this point and must increase without bound at this end we are done. Here is a sketch of the graph. © 2007 Paul Dawkins 260 http://tutorial.math.lamar.edu/terms.aspx College Algebra Example 3 Sketch the graph of P ( x ) = - x 5 + 4 x 3 . Solution As with the previous example we’ll first need to factor this as much as possible. P ( x ) = - x 5 + 4 x 3 = - ( x5 - 4 x3 ) = - x3 ( x 2 - 4 ) = - x 3 ( x - 2 ) ( x + 2 ) Notice that we first factored out a minus sign to make the rest of the factoring a little easier. Here is a list of all the zeroes and their multiplicities. x = -2 ( multiplicity 1) x=0 x=2 ( multiplicity 3) ( multiplicity 1) So, all three zeroes correspond to x-intercepts that actually cross the x-axis since all their multiplicities are odd, however, only the x-intercept at x = 0 will cross the x-axis flattened out. The y-intercept is ( 0, 0 ) a...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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