SOLUTION: 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?
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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?
The statement of the problem allows different interpretations.
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.
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)
With the given function, replacing x with (-x) results in no change, since (-x)^2 is the same as x^2.
But we get different functions depending on whether the shift up by 7 is before or after the stretch by a factor of 9.
(1) If the given transformations are the final results, then the function value is multiplied by 9 and then increased by 7:
(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:
