document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091305>Question 1091305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the function y=5/2sin(1/2x-22.5 degrees)-2 , State the transformations, in the order you would apply them. 													[2]\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706734 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13216)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=706734\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>First, you need to modify the argument for sine so that it is in the form p(x-q); then the q is the horizontal shift and the p determines the horizontal stretch or compression.  So write the function as<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%285%2F2%29sin%28%281%2F2%29%28x-45%29%29-2 ALIGN=MIDDLE  ALT=\"y+=+%285%2F2%29sin%28%281%2F2%29%28x-45%29%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The standard form for this kind of function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28a%29sin%28%28b%29%28x-c%29%29%2Bd ALIGN=MIDDLE  ALT=\"y+=+%28a%29sin%28%28b%29%28x-c%29%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Where<BR>\n" );
document.write( "a is the vertical stretch;<BR>\n" );
document.write( "b determines the horizontal stretch;<BR>\n" );
document.write( "c is the horizontal shift; and<BR>\n" );
document.write( "d is the vertical shift<br><BR>\n" );
document.write( "The order in which the transformations are applied is the order in which you would evaluate the expression for a given input value.<br><BR>\n" );
document.write( "The innermost parentheses is (x-45); so apply the horizontal shift first.<BR>\n" );
document.write( "Next is the multiplication (of the angle) by 1/2; so apply the horizontal stretch second.<BR>\n" );
document.write( "Next is the multiplication (of the sine) by 5/2; so apply the vertical stretch third.<BR>\n" );
document.write( "And last is subtracting 2, which is the same as adding -2, so apply the vertical shift last.<BR>\n" );
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