document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020077>Question 1020077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show all work.	\r<BR>\n" );
document.write( "\n" );
document.write( "Consider the function \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x)=x^5-x^3<BR>\n" );
document.write( "a	Determine the behaviors as x&#8594;&#8734;  and as x&#8594;-&#8734;<BR>\n" );
document.write( "b	Find all zeros. What is the multiplicity of roots (zeros)?<BR>\n" );
document.write( "c	When will the function cross the x-axis? When will it cross the y-axis?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636017 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Please show all work.	<BR>\n" );
document.write( "Consider the function \r<BR>\n" );
document.write( "\n" );
document.write( "f(x)=x^5-x^3<BR>\n" );
document.write( "a	Determine the behaviors as x&#8594;&#8734; and as x&#8594;-&#8734;<BR>\n" );
document.write( "The highest power term determins the answer::<BR>\n" );
document.write( "Since x^5 goes to +oo as x goes to +oo, f(x) goes to +oo<BR>\n" );
document.write( "Since x^6 goes to -oo as x goes to -oo, f(x) goes to -oo<BR>\n" );
document.write( "------------------------------------------------------------------------<BR>\n" );
document.write( "b	Find all zeros. What is the multiplicity of roots (zeros)?<BR>\n" );
document.write( "Solve x^5-x^3 = 0<BR>\n" );
document.write( "x^3(x^2-1) = 0<BR>\n" );
document.write( "x = 0 with multiplicity 3<BR>\n" );
document.write( "x = 1 with multiplicity 1<BR>\n" );
document.write( "x = -1 with multtiplicity 1<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "c When will the function cross the x-axis?<BR>\n" );
document.write( "Solve x^5 - x^3 = 0 to answer that question.<BR>\n" );
document.write( "---------------- <BR>\n" );
document.write( "When will it cross the y-axis?<BR>\n" );
document.write( "Let x = 0, then f(0) = 0<BR>\n" );
document.write( "Ans (0,0)<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );