document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141495>Question 1141495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> without graphing  determine the amplitude, period, domain, and range of the function of the function y=-2.3sin (5x)+7  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762066 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=762066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the basic formula is y = a * sin(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=-2.3sin (5x)+7\r<BR>\n" );
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document.write( "the amplitude is 2.3\r<BR>\n" );
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document.write( "the frequency is 5\r<BR>\n" );
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document.write( "the vertical displacement is 7\r<BR>\n" );
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document.write( "the period is equal to 360 degrees / the frequency.<BR>\n" );
document.write( "that makes the period equal to 360 / 5 = 72 degrees.\r<BR>\n" );
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document.write( "since the vertical displacement is 7, the center line of the sine wave is at y = 7.\r<BR>\n" );
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document.write( "this makes the range of the sine wave equal to 7 - 2.3 to 7 + 2.3.\r<BR>\n" );
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document.write( "that makes it equal to 4.7 <= y <= 9.3.\r<BR>\n" );
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document.write( "the domain is all real values of x, since there are no restrictions on the value of x.\r<BR>\n" );
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document.write( "that makes the domain - infinity < x < + infinity.\r<BR>\n" );
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document.write( "all this was done without graphing.\r<BR>\n" );
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document.write( "however, to confirm whether the information supplied is correct, i drew some graphs that are shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/052601.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the graph confirms what i gold you up top.\r<BR>\n" );
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document.write( "the period is 72 degrees.<BR>\n" );
document.write( "the frequency is 5<BR>\n" );
document.write( "the amplitude is 2.3<BR>\n" );
document.write( "the range is y = 4.7 to 9.3<BR>\n" );
document.write( "the center line is y = 7<BR>\n" );
document.write( "the domain is all real values of x.<BR>\n" );
document.write( "the sine wave repeats every 72 degrees.<BR>\n" );
document.write( "the domain would be 0 <= x <= 72 plus or minus k * 72, where k is a positive integer.<BR>\n" );
document.write( "that makes the domain all real values of x because the value of x goes infinitely on to the right or to the left of the basic period of 0 to 72 degrees.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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