document.write( "Question 1142684: Given that f(x)=x^(2)+7. In the space below, type a function that would shift f(x) up 7 units, vertically stretch the function by a factor of 9, and reflect is across the y-axis?\r
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Algebra.Com's Answer #763408 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The statement of the problem allows different interpretations.

\n" ); document.write( "If the transformations are to be performed one at a time in the given order, the resulting function will be different than if the given transformations are the end result.

\n" ); document.write( "The shift up adds 7 to the function value
\n" ); document.write( "The vertical stretch by a factor of 9 multiplies the function value by 9
\n" ); document.write( "The reflection across the y-axis changes x to (-x)

\n" ); document.write( "With the given function, replacing x with (-x) results in no change, since (-x)^2 is the same as x^2.

\n" ); document.write( "But we get different functions depending on whether the shift up by 7 is before or after the stretch by a factor of 9.

\n" ); document.write( "(1) If the given transformations are the final results, then the function value is multiplied by 9 and then increased by 7:
\n" ); document.write( " $\"f%28x%29+=+9%28%28-x%29%5E2%2B7%29%2B7+=+9x%5E2%2B70\"$

\n" ); document.write( "(2) If the transformations are to be performed in the order given, the the function value is increased by 7 and then multiplied by 9:
\n" ); document.write( " $\"f%28x%29+=+9%28%28-x%29%5E2%2B7%2B7%29+=+9x%5E2%2B126\"$ \n" ); document.write( "

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