document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=347657>Question 347657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have tried so many different things on this problem, thinking through why they would be what they are and I still got them wrong. Please help me understand. This is what I put for each in order, it is what I was convinced the answer was. (F,T,T,F,F,F,F) Why are any of these wrong?\r<BR>\n" );
document.write( "\n" );
document.write( "(1 pt) Let the function f be defined by f(x) = {1}/{sqrt{1-x^2}}. Indicate whether the following statements are True (T) or False (F). You must get all answers correct in order to receive credit.<BR>\n" );
document.write( "___1. f(x) is never positive.<BR>\n" );
document.write( "___2. 1 is in the domain of f<BR>\n" );
document.write( "___3. 0 is in the domain of f<BR>\n" );
document.write( "___4. f(x) is never negative.<BR>\n" );
document.write( "___5. All negative real numbers are in the domain of f<BR>\n" );
document.write( "___6. f(x) is never zero.<BR>\n" );
document.write( "___7. All positive real numbers are in the domain of f<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 #248526 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=248526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. f(x) is never positive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is false since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281-x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%281-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is always nonnegative.\r<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "2. 1 is in the domain of f\r<BR>\n" );
document.write( "\n" );
document.write( "This is false since x=1 makes the denominator equal to zero.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "3. 0 is in the domain of f\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is true since the input x=0 yields a real number output.\r<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "4. f(x) is never negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is true since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281-x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%281-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is always nonnegative.\r<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5. All negative real numbers are in the domain of f\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "False. The domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3Cx%3C1 ALIGN=MIDDLE  ALT=\"-1%3Cx%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So clearly, a number like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-10 ALIGN=MIDDLE  ALT=\"x=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT in the domain.\r<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "6. f(x) is never zero.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is true as the numerator will never equal zero.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "7. All positive real numbers are in the domain of f\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "False. Again, the domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3Cx%3C1 ALIGN=MIDDLE  ALT=\"-1%3Cx%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Jim </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );