document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078505>Question 1078505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the graph of y=cos(pix)-2 is shifted up by 3 units, left by 1 unit and vertically stretched by a factor of 2, what will be new equation describing it?(explain too please)<BR>\n" );
document.write( "a) y= 2cos(pi(x-1)) -5<BR>\n" );
document.write( "b) y=cos(2pi(x-1)) +1<BR>\n" );
document.write( "c) y=cos(2pix +1)-5<BR>\n" );
document.write( "d) y=2 cos(pi(x+1))+1<BR>\n" );
document.write( "e) none </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692940 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=692940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general formula is:\r<BR>\n" );
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document.write( "y = acos(b(x-c))+d\r<BR>\n" );
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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( "your equation is y = cos(pi * x) - 2\r<BR>\n" );
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document.write( "shift it up 3 units and it becomes y = cos(pi * x) + 1\r<BR>\n" );
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document.write( "shift it to the left 1 unit and it becomes y = cos(pi * (x+1) + 1\r<BR>\n" );
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document.write( "stretch it vertically by a factor of 2 and it becomes y = 2 * cos(pi * (x+1)) + 1\r<BR>\n" );
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document.write( "my first graph is the original function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/042701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "my second graph shifts the function from the first graph up by 3 units.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/042702.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "my third graph shifts the function from the second graph to the left 1 unit.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/042703.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "my fourth graph vertically expands the third graph by a factor of 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/042704.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the fourth graph is your solution.\r<BR>\n" );
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document.write( "that looks like your selection d.\r<BR>\n" );
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document.write( "note that:\r<BR>\n" );
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document.write( "frequency is equal to 2pi / period.\r<BR>\n" );
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document.write( "since the frequency of your first graph is pi radians, then the period is 2pi/pi = 2 radians.\r<BR>\n" );
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document.write( "you get one complete cycle of the cosine wave in 2 radians as shown on the graph.\r<BR>\n" );
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document.write( "in the first graph:\r<BR>\n" );
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document.write( "the horizontal range goes from x = 0 to x = 2<BR>\n" );
document.write( "the center line is y = -2<BR>\n" );
document.write( "the vertical range goes from y = -1 to y = -3\r<BR>\n" );
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document.write( "in the second graph:\r<BR>\n" );
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document.write( "the horizontal range remains at x = 0 to x = 2<BR>\n" );
document.write( "the center line moves up 3 units to y = 1<BR>\n" );
document.write( "the vertical range becomes y = 2 to y = 0\r<BR>\n" );
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document.write( "this is because the graph has been shifted up 3 units.\r<BR>\n" );
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document.write( "in the third graph:\r<BR>\n" );
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document.write( "the horizontal range becomes x = -1 to x = 1<BR>\n" );
document.write( "the center line remains at y = 1<BR>\n" );
document.write( "the vertical range remains at y = 2 to y = 0\r<BR>\n" );
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document.write( "this is because the graph has been shifted to the left 1 unit.\r<BR>\n" );
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document.write( "in the fourth graph:\r<BR>\n" );
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document.write( "the horizontal range remains at x = -1 to x = 1<BR>\n" );
document.write( "the center line remains at y = 1<BR>\n" );
document.write( "the vertical range becomes y = 3 to y = -1\r<BR>\n" );
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document.write( "this is because the vertical range has been multiplied by a factor of 2.\r<BR>\n" );
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document.write( "here's a reference that looks pretty complete.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.mathguide.com/lessons2/GraphingTrig.html\" target = \"_blank\">http://www.mathguide.com/lessons2/GraphingTrig.html</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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