document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=213488>Question 213488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am still unsure when it comes to functions.  I have a question that is as follows:  Is f(x) = x^2 + 2x - 3 a one-to-one function?  Explain your answer.\r<BR>\n" );
document.write( "\n" );
document.write( "When figuring out the problem if f(a) = f(b) then my answer would be no as <BR>\n" );
document.write( "a^2 + 2a - 3 = b^2 + 2b -3 does not factor down to a = b.\r<BR>\n" );
document.write( "\n" );
document.write( "Am I figuring this correctly?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you = Lori </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161291 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=161291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're on the right track. A function is one-to-one if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29=f%28b%29 ALIGN=MIDDLE  ALT=\"f%28a%29=f%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <u>only</u> means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b ALIGN=MIDDLE  ALT=\"a=b\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, if two outputs of a function are equal, then the inputs <u>must</u> be equal for the function to be one-to-one.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So if you think that this function is NOT one-to-one, then simply pick a counter-example to prove this claim false. Let's say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29=f%28b%29=-3 ALIGN=MIDDLE  ALT=\"f%28a%29=f%28b%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plugging this into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B2x-3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > gets us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=x%5E2%2B2x-3 ALIGN=MIDDLE  ALT=\"-3=x%5E2%2B2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now solve for 'x' to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So if we plug in either 0 or -2 into f(x), we'll get -3 as an output. Ie. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=f%28-2%29=-3 ALIGN=MIDDLE  ALT=\"f%280%29=f%28-2%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C%3E-2 ALIGN=MIDDLE  ALT=\"0%3C%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the function is NOT one-to-one. So you are correct.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );