document.write( "Question 916789: Suppose the point (4, -6) is on the graph of y = f(x). Which of the following is a point on the graph of y = 3f(x – 2) + 4? \n" ); document.write( "

Algebra.Com's Answer #556396 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "The old graph was $\"y+=+f%28x%29\"$ . \r
\n" ); document.write( "\n" ); document.write( "The new graph, after transformation, is $\"y\"$ ' = $\"3f\"$ ( $\"x\"$ '- $\"2\"$ )+ $\"4+\"$ , which can also be written as ( $\"y\"$ ' - $\"4\"$ )/ $\"3\"$ = $\"f\"$ ( $\"x\"$ ' - $\"2\"$ ). \r
\n" ); document.write( "\n" ); document.write( "(Here the accent sign ' denotes \"new coordinate\"; and not differentation or derivative of a variable or anything.) \r
\n" ); document.write( "\n" ); document.write( "Hence the transformation is \r
\n" ); document.write( "\n" ); document.write( " $\"x\"$ = $\"x\"$ ' - $\"2+\"$
\n" ); document.write( " $\"y\"$ = ( $\"y\"$ ' - $\"+4\"$ )/ $\"3\"$ \r
\n" ); document.write( "\n" ); document.write( "The old coordinates were ( $\"x\"$ , $\"+y\"$ ) = ( $\"4\"$ , $\"-6\"$ ). \r
\n" ); document.write( "\n" ); document.write( "So the new coordinates ( $\"x\"$ ', $\"y\"$ ') are found by solving \r
\n" ); document.write( "\n" ); document.write( " $\"4\"$ = $\"x\"$ ' - $\"2\"$ => $\"4%2B2\"$ = $\"x\"$ ' => $\"6\"$ = $\"x\"$ ' \r
\n" ); document.write( "\n" ); document.write( " $\"-6\"$ = ( $\"y\"$ ' - $\"4\"$ )/ $\"3\"$ => $\"-6%2A3\"$ = $\"y\"$ ' - $\"4\"$ => $\"-18\"$ = $\"y\"$ ' - $\"4\"$ => $\"-18%2B4\"$ = $\"y\"$ ' => $\"-14\"$ = $\"y\"$ ' \r
\n" ); document.write( "\n" ); document.write( "Hence the new coordinates are ( $\"x\"$ ', $\"+y\"$ ') = ( $\"6\"$ , $\"-14\"$ ). \r
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