document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=215676>Question 215676</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1- Give the new coordinates if the point (4,-6) is transformed in the following manner: reflected across the y-axis, vertically compressed by a factor of one-half, and translated 6 units to the right. Show work.\r<BR>\n" );
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document.write( "2- A rectangle is enclosed by the x-axis and the graph of y= 3-|1/2 x|, with two vertices on the x-axis and two vertices on the given function. What are the dimensions of the rectangle that will yield the maximum area?\r<BR>\n" );
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document.write( "3- Suppose f is a function such that for all real number x. f(x-4) = x^2-2x. Find f(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163043 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Give the new coordinates if the point (4,-6) is transformed in the following manner: reflected across the y-axis: (4,6)<BR>\n" );
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document.write( "vertically compressed by a factor of one-half: (4,3)<BR>\n" );
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document.write( " and translated 6 units to the right: (10,3)<BR>\n" );
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document.write( "2- A rectangle is enclosed by the x-axis and the graph of y= 3-|1/2 x|, with two vertices on the x-axis and two vertices on the given function. What are the dimensions of the rectangle that will yield the maximum area?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C3-abs%280.5x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C3-abs%280.5x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let the base vertices be (-x,0) and (x,0).<BR>\n" );
document.write( "The base width = 2x<BR>\n" );
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document.write( "altitude = 3 -(1/2)x<BR>\n" );
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document.write( "Area = 2x(3-(1/2)x) = -x^2+6x<BR>\n" );
document.write( "Maximum occurs when x = -b/2a = -6/(-2) = 3<BR>\n" );
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document.write( "A(3) = -(3)^2 + 6*3 = 9 (That is the maximum area)<BR>\n" );
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document.write( "3- Suppose f is a function such that for all real number x. f(x-4) = x^2-2x. Find f(x)<BR>\n" );
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document.write( "Since f(x) had moved 4 to the right when it became f(x-4)<BR>\n" );
document.write( "replace x by (x+4) to find f(x).  <BR>\n" );
document.write( "f(x) = (x+4)^2-2(x+4) = x^2+8x+16-2x-8 = x^2+6x+8<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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