document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=510855>Question 510855</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi, i need help learning how to graph tangent functions<BR>\n" );
document.write( ".. the function i was given was y= tan (x- pi/4)<BR>\n" );
document.write( ".. if anyone you help explain it to me and even show a graph,<BR>\n" );
document.write( "that would be great!<BR>\n" );
document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341985 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=341985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graphing tangent functions<BR>\n" );
document.write( "I don't have the means to draw a graph but maybe I can show you how.<BR>\n" );
document.write( "given function: y= tan (x- pi/4)<BR>\n" );
document.write( "Standard equation for tangent function: y=tan(Bx-C), period=&#960;/B, Phase shift=C/B<BR>\n" );
document.write( "For given function:<BR>\n" );
document.write( "B=1<BR>\n" );
document.write( "period=&#960;/1=&#960;<BR>\n" );
document.write( "1/4 period=&#960;/4<BR>\n" );
document.write( "phase shift=C/B=(&#960;/4)/1=&#960;/4 (to the right)<BR>\n" );
document.write( "Graphing for one period:<BR>\n" );
document.write( "Without a phase shift, the curve of tanx would start at -&#960;/2 and end at &#960;/2<BR>\n" );
document.write( "tan(-&#960;/2)=-&#8734;(asymptote)<BR>\n" );
document.write( "tan(-&#960;/4)=-1<BR>\n" );
document.write( "tan(0)=0<BR>\n" );
document.write( "tan(&#960;/4)=1<BR>\n" );
document.write( "tan(&#960;/2)=&#8734;(asymptote)<BR>\n" );
document.write( "so, now you have these ordered pairs to draw the basic tanx function:<BR>\n" );
document.write( "(-&#960;/2, -&#8734;), (-&#960;/4,-1), (0,0), (&#960;/4,1), (&#960;/2,&#8734;)<BR>\n" );
document.write( "But since the curve has shifted &#960;/4 radians, &#960;/4 must be added to each x-coordinate to plot the given tan function, y= tan (x- pi/4), as follows:<BR>\n" );
document.write( "(-&#960;/4, -&#8734;), (0,-1), (&#960;/4,0), (&#960;/2,1), (3&#960;/4,&#8734;) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );