document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57873>Question 57873</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0130655929/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 11. is the function f(x)=x^5+4x-7 even, odd, or neither?\r<BR>\n" );
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document.write( "12. determine the intervals over which f(x)=(x^2-4)^2 is increasing, decreasing, or constant. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #39541 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=39541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 11. is the function f(x)=x^5+4x-7 even, odd, or neither?<BR>\n" );
document.write( "If f(-x)=f(x) the function is even.<BR>\n" );
document.write( "If f(-x)=f(x)  the function is odd<BR>\n" );
document.write( "f(-x)=(-x)^5+4(-x)-7<BR>\n" );
document.write( "f(-x)=-x^5-4x-7  <---Neither<BR>\n" );
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document.write( "A short cut is to look at all of the exponents of the variables, think of any constants like -7 as being -7x^0.  If all of the exponents are even, the function is even, if all of the exponents are odd, the function is odd, if there is a mixture of any kind, it's neither.  <BR>\n" );
document.write( "The variables of this equation are, 5,1, and 0.  Neither. \r<BR>\n" );
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document.write( "12. determine the intervals over which f(x)=(x^2-4)^2 is increasing, decreasing, or constant.<BR>\n" );
document.write( "If you are in calculus, you find this out through taking derivatives.  Let me know if that's the case:<BR>\n" );
document.write( "If you're in algebra or algebra II the  most teachers are content to let you use your graphing calculators to solve these, using the max, min functions.<BR>\n" );
document.write( "Here's the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-5%2C20%2C%28x%5E2-4%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-5%2C20%2C%28x%5E2-4%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As you can see, <BR>\n" );
document.write( "the Graph is increasing from x=(-2,0)U(2,infinity)<BR>\n" );
document.write( "The graph is decreasing from x=(-infinity,-2)U(0,2)  <BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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