Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the y axis, followed by a translation 2 units left of the graph of f(x)=x^2-x+1. Write a rule for g. G(x)= ?

The required polynomial is .

The given question solved in the following steps.

        So, after reflection, the new polynomial is  

           So, the new polynomial g(x)        

The required value of g(x) is .

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First, let's write the general transformations:

a) A vertical stretch by a factor of 3.

f(x) ---> 3*f(x)

b) A reflection in the y-axis.

3*f(x) > 3*f(-x)

c) A translation of 2 units to the left.

3*f(-x) > 3*f(-x + 2)

then we know that:

g(x) = 3*f(-x + 2)

and f(x) = x^2 - x + 1

Then:

g(x) = 3*( (-x + 2)^2 - (-x + 2) + 1)

g(x) = 3*( x^2 - 4*x + 4 +x - 2 + 1) = 3*(x^2 - 3*x + 3)

g(x) = 3*x^2 - 9*x - 9

answer: 48

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