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 #846156 by mccravyedwin(406) $\"\"$ $\"About$

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document.write( "This type of problem requires knowing how to shift graphs right and \r\n" );
document.write( "left, stretching and shrinking, both horizontally and vertically.\r\n" );
document.write( "It is also necessary that the transformations are done in the right\r\n" );
document.write( "order, multiplications first then additions and subtractions.\r\n" );
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document.write( "Vertical transformations are done to the function itself, the whole\r\n" );
document.write( "\"right side\".\r\n" );
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document.write( "Vertical transformations are as they seem, adding and subtracting\r\n" );
document.write( "to shift up and down, multiplying by factors > 1 to stretch, \r\n" );
document.write( "multiplying by factors < 1 to shrink.\r\n" );
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document.write( "Horizontal transformation are done to x.\r\n" );
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document.write( "Horizontal transformation are \"backward\" from what they seem, adding\r\n" );
document.write( "to x to shift left, subtracting from x to shift right, multiplying\r\n" );
document.write( "by the reciprocal of factors > 1 to stretch, and multiplying by \r\n" );
document.write( "factors > 1 to shrink.\r\n" );
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document.write( "Since the x-value of f(x) is 'a' and the x-value on g(x) is '2a+1',\r\n" );
document.write( "the factor of 2 in '2a+1' means that the graph of f(x) is stretched \r\n" );
document.write( "horizontally by a factor of 2, which means we multiply x by the\r\n" );
document.write( "reciprocal of 2, which is 1/2. \r\n" );
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document.write( "So doing only that horizontal stretch would give us \r\n" );
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document.write( "Then the term +1 in '2a+1' means that we shift the graph right by 1 unit,\r\n" );
document.write( "which means we subtract 1 from x or, add -1 to x\r\n" );
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document.write( "so doing that would give us \r\n" );
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document.write( "That finishes doing everything required to do to the x-coordinate.\r\n" );
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document.write( "Now the 3 factor in \"3b\" means that the graph is stretched vertically by\r\n" );
document.write( "a factor of 3, so we multiply the entire function by 3.\r\n" );
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document.write( "That gives us \r\n" );
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document.write( "So the answer is\r\n" );
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document.write( "Edwin

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