Question 1142684
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The statement of the problem allows different interpretations.<br>
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.<br>
The shift up adds 7 to the function value
The vertical stretch by a factor of 9 multiplies the function value by 9
The reflection across the y-axis changes x to (-x)<br>
With the given function, replacing x with (-x) results in no change, since (-x)^2 is the same as x^2.<br>
But we get different functions depending on whether the shift up by 7 is before or after the stretch by a factor of 9.<br>
(1) If the given transformations are the final results, then the function value is multiplied by 9 and then increased by 7:
{{{f(x) = 9((-x)^2+7)+7 = 9x^2+70}}}<br>
(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:
{{{f(x) = 9((-x)^2+7+7) = 9x^2+126}}}