document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166141>Question 1166141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you compare the function y=5(1/2)^x to the exponential parent function   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790627 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=790627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe, based on the reference i found at <a  rel=nofollow HREF= \"\" target = \"_blank\"></a>, that the parent function is y = b^x and that parent function can be transformed by the form of y = a * b^(x-h) + k.\r<BR>\n" );
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document.write( "a is the vertical transformation, b is the base, x is the exponent, h is the horizontal shift, k is the vertical shift.\r<BR>\n" );
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document.write( "the vertical transformation will either expand (a is >  1) or contract (a is less than 1) or reflect the the graph about the x-axis.\r<BR>\n" );
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document.write( "(x-h) will shift the graph to the left (h is positive) or to the right (h is negative).\r<BR>\n" );
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document.write( "k will shift the graph either up (k is positive) or down (k is negative).\r<BR>\n" );
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document.write( "your equation is y = 5 * (1/2) ^ x.\r<BR>\n" );
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document.write( "i believer the base function would be y = b^x where be = 1/2.\r<BR>\n" );
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document.write( "the graph of that function is shown below:\r<BR>\n" );
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document.write( "y = (1/2) ^ 0 crosses the y-axis at y = 1, since any base raised to the power of 0 will be equal to 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/092901.jpg\" >\r<BR>\n" );
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document.write( "the function of y = 5 * (1/2) ^ x appears to be the same function that has been expanded because a is positive.\r<BR>\n" );
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document.write( "there is no horizontal shift (h = 0) and there is no vertical shift (k = 0).\r<BR>\n" );
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document.write( "the only change is that the value of y is 5 times greater than it would be with the base function for the same value of x.\r<BR>\n" );
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document.write( "in the following graph, the value of a = 5 expands the graph by 5 times what the value of y would be in the base graph.\r<BR>\n" );
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document.write( "at x = -1, the expanded graph y value is 10 rather than 2; at x = 0, the expanded y value is 5 rather than 1; at x = 2, the expanded graph y value is 1.25 rather than .25.\r<BR>\n" );
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document.write( "in each case, the expanded y value is 5 times the base y value because the value of a is 5 rather than 1. \r<BR>\n" );
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document.write( "1 is the default value of a.<BR>\n" );
document.write( "if the value of a is not shown, it is same as if it is equal to 1.\r<BR>\n" );
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document.write( "here is the graph of the expanded function compared to the base function.\r<BR>\n" );
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document.write( "the base function is in red.<BR>\n" );
document.write( "the expanded function is in blue.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/092902.jpg\" >\r<BR>\n" );
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document.write( "here is an excellent reference on the subject.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://mathbitsnotebook.com/Algebra2/Exponential/EXExpFunctions.html\" target = \"_blank\">https://mathbitsnotebook.com/Algebra2/Exponential/EXExpFunctions.html</a>\r<BR>\n" );
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document.write( "the reference to other information concerning high school math subject from this site can be found at <a  rel=nofollow HREF= \"http://mathbitsnotebook.com/\" target = \"_blank\">http://mathbitsnotebook.com/</a>\r<BR>\n" );
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