document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159754>Question 1159754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4. Graph f(x) = 3sin(2x) + 2 over the interval [0, 2π] on the set of axes below. (4 points)\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 #782833 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=782833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3sin%282x%29%2B2 ALIGN=MIDDLE  ALT=\"y+=+3sin%282x%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Graph the function by looking at how the parent function sin(x) is modified.<br><BR>\n" );
document.write( "The order of the transformations is the order in which you would evaluate the function for a given value of x.  The \"3\" is a multiplication; the \"(2x)\" is in parentheses; the \"+2\" is addition.  According to standard rules of order of operations, the order is (1) parentheses, (2) multiplication, and (3) addition.<br><BR>\n" );
document.write( "Here is the graph of the parent function sin(x):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C200%2C0%2C2pi%2C-6%2C6%2Csin%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C200%2C0%2C2pi%2C-6%2C6%2Csin%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "First transformation: parentheses<br><BR>\n" );
document.write( "sin(2x) compared to sin(x) means the graph completes two periods instead of one on [0,2pi] -- i.e., the period of the function is cut in half, from 2pi to pi.  Note this is often viewed as a horizontal compression by a factor of 2.<br><BR>\n" );
document.write( "Here is the graph of sin(2x):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C200%2C0%2C2pi%2C-6%2C6%2Csin%282x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C200%2C0%2C2pi%2C-6%2C6%2Csin%282x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Second transformation: multiplication<br><BR>\n" );
document.write( "3sin(2x) compared to sin(2x) stretches the graph vertically by a factor of 3.<br><BR>\n" );
document.write( "Here is the graph of 3sin(2x):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C200%2C0%2C2pi%2C-6%2C6%2C3sin%282x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C200%2C0%2C2pi%2C-6%2C6%2C3sin%282x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Third transformation: addition<br><BR>\n" );
document.write( "3sin(2x)+2 compared to 3sin(2x) translates the graph vertically by 2 units.<br><BR>\n" );
document.write( "Here is the graph of 3sin(2x)+2:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C200%2C0%2C2pi%2C-6%2C6%2C3sin%282x%29%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C200%2C0%2C2pi%2C-6%2C6%2C3sin%282x%29%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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