document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203784>Question 1203784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch two periods of the graph for the following function.<BR>\n" );
document.write( "f(x) = 5sec(3x)<BR>\n" );
document.write( "Identify the stretching factor and period.<BR>\n" );
document.write( "Identify the asymptotes in the displayed domain of the graph you selected above. (Enter your answers as a comma-separated list of equations.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839635 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839635\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> euation is f(x) = 5sec(3x)<BR>\n" );
document.write( "general form is f(x) = a * sec(b * (x-c)) + d<BR>\n" );
document.write( "a is the amplitude.<BR>\n" );
document.write( "b is the frequency.<BR>\n" );
document.write( "c is the horizontal shift.<BR>\n" );
document.write( "d is the vertical shift.\r<BR>\n" );
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document.write( "i believe they are referring to the amplitude as the stretching factor.<BR>\n" );
document.write( "the default is 1 unit above and 1 unit below the center horizontal line.<BR>\n" );
document.write( "when it is 5, the amplitude is 5 times as much above and below the horizontal line.\r<BR>\n" );
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document.write( "the normal period of the secant function is 360 degrees.<BR>\n" );
document.write( "the freuency for the secant function is equal to 360 / the period.<BR>\n" );
document.write( "the period for the secant function is equal to 360 / the frequency.<BR>\n" );
document.write( "the frequency for this secant function is 3.<BR>\n" );
document.write( "the period is therefore 360 / 3 = 120 degrees.\r<BR>\n" );
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document.write( "there is no horizontal shift.<BR>\n" );
document.write( "here is no vertical shift.\r<BR>\n" );
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document.write( "the graph of this runction is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092103.jpg\">\r<BR>\n" );
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document.write( "the secant function is in red.<BR>\n" );
document.write( "the cosine function is in blue.\r<BR>\n" );
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document.write( "you want the secant function.<BR>\n" );
document.write( "i only showed the cosine function because the secant function is equal to 1 divided by the cosine function.<BR>\n" );
document.write( "i thought it would be easier for you to see that it is the reciprocal of the cosine function that way.<BR>\n" );
document.write( "the graph that you want is the red graph.\r<BR>\n" );
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document.write( "the asymptotes are at 0 degrees and at 120 degrees.<BR>\n" );
document.write( "that's where the cosine function = 0.<BR>\n" );
document.write( "since the secant function is 1 / cosine function, that's where the secant function is undefined.<BR>\n" );
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