document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=401115>Question 401115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to do the following problems:\r<BR>\n" );
document.write( "\n" );
document.write( "1. Let t(x) = { 1-3x for x <= -1<BR>\n" );
document.write( "              { 1+x^2 for x > -1<BR>\n" );
document.write( "Determine t(&#8722;3), t(&#8722;1), t(0), and t(5).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. Graph f(x) = { |x| for x < 2<BR>\n" );
document.write( "                { 1 for 2 <= x < 4<BR>\n" );
document.write( "                { 1 &#8722; x for x >= 4\r<BR>\n" );
document.write( "\n" );
document.write( "3. Draw the graph of y = &#8722;2|x + 1| &#8722; 4. Do not do this by plotting points. Instead construct a sequence of five graphs and get from one graph to the next by applying an appropriate<BR>\n" );
document.write( "transformation.\r<BR>\n" );
document.write( "\n" );
document.write( "4. Same as problem 3 for the function y = &#8722;4 sqrt x + 2 + 1.\r<BR>\n" );
document.write( "\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 #283834 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=283834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Let t(x) = { 1-3x for x <= -1<BR>\n" );
document.write( "..............{ 1+x^2 for x > -1<BR>\n" );
document.write( "Determine <BR>\n" );
document.write( "t(&#8722;3) = 1-3(-3) = 10<BR>\n" );
document.write( "t(&#8722;1) = 1-3(-1) = 4 <BR>\n" );
document.write( "t(0) = 1+0^2 = 1 <BR>\n" );
document.write( "t(5) = 1+5^2 = 26<BR>\n" );
document.write( "================================ \r<BR>\n" );
document.write( "\n" );
document.write( "2. Graph f(x) = { |x| for x < 2<BR>\n" );
document.write( "................{ 1 for 2 <= x < 4<BR>\n" );
document.write( "................{ 1 &#8722; x for x >= 4\r<BR>\n" );
document.write( "\n" );
document.write( "Note: Can't show this segmented graph on this site.<BR>\n" );
document.write( "================================<BR>\n" );
document.write( " <BR>\n" );
document.write( "3. Draw the graph of y = &#8722;2|x + 1| &#8722; 4. Do not do this by plotting points. Instead construct a sequence of five graphs and get from one graph to the next by applying an appropriate transformation.<BR>\n" );
document.write( "1st: Graph y = |x|<BR>\n" );
document.write( "2nd: Shift 1 to the right to get |x+1|<BR>\n" );
document.write( "3rd: Reflect in the x-axis<BR>\n" );
document.write( "4th: Multiply all the y-values by 2<BR>\n" );
document.write( "5th: Shift all the points down 4 units.<BR>\n" );
document.write( "===============\r<BR>\n" );
document.write( "\n" );
document.write( "4. Same as problem 3 for the function y = &#8722;4 sqrt (x + 2) + 1. <BR>\n" );
document.write( "1st: Graph y = sqrt(x)<BR>\n" );
document.write( "2nd: Shift 2 to the left<BR>\n" );
document.write( "3rd: Reflect in the x-axis<BR>\n" );
document.write( "4th: Multiply all the y-values by 4<BR>\n" );
document.write( "5th: Shift all the points up 1 unit.<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "===========<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );