SOLUTION: Hi, I am having trouble with transformations and I hope someone can help me. The problem states: if f(x)=x^2, then write g(x) so that it translates f(x) in the following way: refl

Question 1088568: Hi, I am having trouble with transformations and I hope someone can help me. The problem states: if f(x)=x^2, then write g(x) so that it translates f(x) in the following way: reflect across the x-axis, shift vertically up 7 units, shift horizontally left 4 units. I believe the shift up will be x^2+7 and the shift left 4 will be (x+4), but I have no idea how to correctly write these. Would it be g(x)=x^2+7(x^2+4)? Thanks for any help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Hi, I am having trouble with transformations and I hope someone can help me. The problem states: if f(x)=x^2, then write g(x) so that it translates f(x) in the following way: reflect across the x-axis, shift vertically up 7 units, shift horizontally left 4 units. I believe the shift up will be x^2+7 and the shift left 4 will be (x+4), but I have no idea how to correctly write these. Would it be g(x)=x^2+7(x^2+4)? Thanks for any help!
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Start:: f(x) = x^2
reflect across the x-axis to get
h(x) = -x^2
shift vertically up 7 units to get
p(x) = -x^2 + 7
shift horizontally left 4 units to get
g(x) = -(x-4)^2 + 7
--------------------------
Cheers,
Stan H.
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