document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126972>Question 1126972</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If N represents the set of natural numbers, and the function f: N &#8594; N such that f(x)=3x. Is the function surjective? injective? bijective? Explain.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743328 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3x ALIGN=MIDDLE  ALT=\"f%28x%29+=+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=injective ALIGN=MIDDLE  ALT=\"injective\"   DISABLED_style= \"max-width:90%; height:auto;\" > (one-to-one)=> your answer\r<BR>\n" );
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document.write( "Injective means we won't have two or more \"A\"s pointing to the same \"B\"<BR>\n" );
document.write( "\"Injective\" (one-to-one)<BR>\n" );
document.write( "In fact we can do a \"Horizontal Line Test\":<BR>\n" );
document.write( "To be Injective, a Horizontal Line should never intersect the curve at 2 or more points.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3x ALIGN=MIDDLE  ALT=\"f%28x%29+=+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > surjective<BR>\n" );
document.write( "BUT <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3x ALIGN=MIDDLE  ALT=\"f%28x%29+=+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the set of natural numbers natural numbers to natural numbers is not surjective, because, for example, no member in natural numbers can be mapped to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > by this function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3x ALIGN=MIDDLE  ALT=\"f%28x%29+=+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > bijective<BR>\n" );
document.write( "Bijective means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=both ALIGN=MIDDLE  ALT=\"both\"   DISABLED_style= \"max-width:90%; height:auto;\" > Injective and Surjective together.\r<BR>\n" );
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