document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137308>Question 1137308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help making the equations\r<BR>\n" );
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document.write( "10. A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final graph.\r<BR>\n" );
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document.write( "10a. f(x) = x^3; shift upward 3 units and shift 2 units to the right.\r<BR>\n" );
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document.write( "10b. f(x) = sqrtx; reflect in the y-axis, shrink vertically by a factor of 1/2, and shift upward 2 units.\r<BR>\n" );
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document.write( "10c. f(x) = |x|; shift to the left 1 unit, stretch vertically by a factor of 3, and shift upward 5 units.\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 #755184 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=755184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 10a. f(x) = x^3; shift upward 3 units and shift 2 units to the right. \r<BR>\n" );
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document.write( "shift up 3 units becomes x^3 + 3<BR>\n" );
document.write( "shift to the right 2 units becomes (x-2)^3 + 3\r<BR>\n" );
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document.write( "here's what happens.\r<BR>\n" );
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document.write( "when x is equal to 0, y = x^3 becomes y = 0^3 which becomes y = 0.<BR>\n" );
document.write( "when x is equal to 0, y = x^3 + 3 becomes y = 0^3 + 3 which becomes y = 0 + 3 which becomes y = 3.<BR>\n" );
document.write( "when x = 2, y = (x-2)^3 + 3 becomes y = 0^3 + 3 which becomes y = 0 + 3 which becomes y = 3.\r<BR>\n" );
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document.write( "here's the progression.\r<BR>\n" );
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document.write( "10b. f(x) = sqrtx; reflect in the y-axis, shrink vertically by a factor of 1/2, and shift upward 2 units. \r<BR>\n" );
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document.write( "here's what happens.\r<BR>\n" );
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document.write( "when x = 5, y = sqrt(x) becomes y = sqrt(5) which becomes y = 2.236 rounded to 3 decimal digits.<BR>\n" );
document.write( "when x = -5, y = sqrt(-x) becomes y = sqrt(-(-5)) which becomes y = sqrt(5) which becomes y =  2.236 rounded to 3 decimal digits.<BR>\n" );
document.write( "when x = -5, y = 1/2 * sqrt(-x) becomes y = 1/2 * sqrt(-(-5)) which becomes y = 1/2 * sqrt(5) which becomes y = 1/2 * 2.236 which becomes y =  1.118 rounded to 3 decimal digits.<BR>\n" );
document.write( "when x = -5, y = 1/2 * sqrt(-x) + 2 becomes y = 1/2 * sqrt(-(-5)) + 2 which becomes y = 1/2 * sqrt(5) + 2 which becomes y = 1/2 * 2.236 + 2 which becomes y = 1.118 + 3 which becomes y = 3.118 rounded to 3 decimal digits.\r<BR>\n" );
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document.write( "here's the progression.\r<BR>\n" );
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document.write( "10c. f(x) = |x|; shift to the left 1 unit, stretch vertically by a factor of 3, and shift upward 5 units. \r<BR>\n" );
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document.write( "here's what happens.\r<BR>\n" );
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document.write( "when x = 1, y = abs(x) becomes y = abs(1) which becomes y = 1.<BR>\n" );
document.write( "when x = 0, y = abs(x+1) becomes y = abs(1) which becomes y = 1.<BR>\n" );
document.write( "when x = 0, y = 3 * abs(x+1) becomes y = 3 * abs(1) which becomes y = 3 * 1 which becomes y = 3.<BR>\n" );
document.write( "when x = 0, y = 3 * abs(x+1) + 5 becomes y = 3 * abs(1) + 5 which becomes y = 3 * 1 + 5 which becomes y = 3 + 5 which becomes y = 8.\r<BR>\n" );
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document.write( "here's the progression.\r<BR>\n" );
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