document.write( "Question 1208030: For each point (a,b) that is on the graph of y = f(x), the point (2a +1, 3b) is plotted, forming the graph of another function y = g(x). As an example, the point (0,2) lies on the graph of y = f(x), so the point (2 • 0 + 1, 3 • 2) = (1, 6) lies on the graph of y = g(x).\r
\n" ); document.write( "\n" ); document.write( "(a) Plot the graph of y = g(x). Include the diagram as part of your solution.\r
\n" ); document.write( "\n" ); document.write( "(b) Express g(x) in terms of f(x).\r
\n" ); document.write( "\n" ); document.write( "(c) Describe the transformations that can be applied to the graph of y = f(x) to obtain the graph of y = g(x). For example, one transformation could be to stretch the graph vertically by a factor of 4.\r
\n" ); document.write( "\n" ); document.write( "The graph: https://artofproblemsolving.com/texer/gbtdafpj \n" ); document.write( "

Algebra.Com's Answer #846159 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Manipulations are hard to understand without visual interpretations.\r\n" );
document.write( "Here is a visual illustration of this problem with the\r\n" );
document.write( "case \r\n" );
document.write( "\r\n" );
document.write( "We begin with \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then we stretched it horizontally by a factor of 2,\r\n" );
document.write( "giving us the graph of\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then we shifted it right 1 unit, giving us the graph of\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then finally we stretched the graph vertically by a factor\r\n" );
document.write( "of 3, giving us the final graph of \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So \r\n" );
document.write( "\r\n" );
document.write( "Here are the graphs of f(x) and g(x), the red one is f(x),\r\n" );
document.write( "and the blue graph is g(x).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The point (4,2) lies on the graph of y = f(x), so the point (2•4+1, 3•2),\r\n" );
document.write( "or (9,6) lies on the graph of y = g(x)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );