arlt111203
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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)= ?

Respuesta :

facundo3141592

Answer:

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

The required polynomial is [tex]3x^{2} +15x+21[/tex].

The given question solved in the following steps.

  • Apply vertical stretch by a factor 3.  You get then the polynomial .

        [tex]f(x) = 3( x^{2} -x+1)[/tex]

  • Reflection in the y-axis is the  change  of x to (-x).

        So, after reflection, the new polynomial is  

           [tex]q(x) = 3((-x)^{2} - (-x) + 1 )\\q(x) = 3(x^{2} + x +1 )\\q(x) = 3x^{2} +3 x+3[/tex]

  •   Translation 2 units left is the change of x by (x+2) in the polynomial.

           So, the new polynomial g(x)        

          [tex]g(x) = 3(x+2)^{2} + 3(x+2) + 3\\\\g(x) = 3(x^{2} +4x+4) + 3x + 6 + 3\\g(x) = 3x^{2} + 12x +12 +3x+ 9\\g(x) = 3x^{2} + 15x + 21[/tex]

The required value of g(x) is [tex]3x^{2} +15x+21[/tex].

For more information about rules of graph click the link given below.

https://brainly.com/question/13838647

             

         

               

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