document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=906931>Question 906931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How does the graph of the function compare to the parent function? Y=5(2)^x+1+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550299 by </B><A HREF=/tutors/aboutme.mpl?userid=AlgebraLady88><B>AlgebraLady88(44)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AlgebraLady88><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=AlgebraLady88><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=550299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation is y= 5(2)^x+1  +3<BR>\n" );
document.write( "The parent function here is y= 2^x \r<BR>\n" );
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document.write( "The parent function is just where the graph y= 5(2)^x+1  +3   originates from.\r<BR>\n" );
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document.write( "We are talking about transformations of exponential functions here.<BR>\n" );
document.write( "Transformations involve translations, reflections, expansions (stretching) or compressions (shrinking) or any combination of these.\r<BR>\n" );
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document.write( "Here's what an equation with transformations look like:\r<BR>\n" );
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document.write( "y= a(b) ^ c(x-h)  + k\r<BR>\n" );
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document.write( "Please note:If a is negative, we will flip the graph over the x axis.\r<BR>\n" );
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document.write( "a describes either a vertical compression or expansion.<BR>\n" );
document.write( "If a> 1, we will have an expansion<BR>\n" );
document.write( "If a< 1 , we will have a compression. \r<BR>\n" );
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document.write( "b describes exponential growth or decay.<BR>\n" );
document.write( "If b>1, we will have growth<BR>\n" );
document.write( "If b is bigger than zero but smaller than one , we will have exponential decay\r<BR>\n" );
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document.write( "c describes horizontal compression or expansion<BR>\n" );
document.write( "  If  c is bigger than zero but smaller than one , we will have expansion<BR>\n" );
document.write( "  If  c >1 , we will have compression<BR>\n" );
document.write( "Note : we do the opposite here\r<BR>\n" );
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document.write( "(x-h) is a horizontal shift(translation) left or right.<BR>\n" );
document.write( "If  the sign in the parenthesis is negative, we will shift right<BR>\n" );
document.write( "If the sign in the parenthesis is positive, we will shift left.<BR>\n" );
document.write( "Note: Notice we do the opposite here too.\r<BR>\n" );
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document.write( "k describes vertical shift (translation) up or down.<BR>\n" );
document.write( "If  sign in front of k is positive, we move the graph up<BR>\n" );
document.write( "If sign in front of k is negative, we move the graph down.\r<BR>\n" );
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document.write( "Rules for dealing with a multi transformational exponential growth such as<BR>\n" );
document.write( "y= 5(2)^ x+1  +3\r<BR>\n" );
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document.write( "1) Do any flipping over the x axis first. This will depend on whether a is negative or not\r<BR>\n" );
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document.write( "2) Do the compressions or expansions next( multiplying and dividing)\r<BR>\n" );
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document.write( "3) Do the translations ( adding and subtracting)\r<BR>\n" );
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document.write( "So, for y= 5(2)^x+1  +3\r<BR>\n" );
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document.write( "we see that y= (2)^x has been vertically expanded by a factor of 5, then translated 1 to the left, and then finally, translated 3 up. <BR>\n" );
document.write( "There is an asymptote at y=3, so you will find the graph approaching y=3 , but not quite touching it. </SPAN>\n" );
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