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Beginning with the graph of f(x) = x2, what transformations are needed to form g of x equals one third times the quantity x plus 3 end quantity squared minus 3 question mark?

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To transform f(x) into g(x) we need to use addition, subtraction and multiplication.

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

We need to transform function f(x)into g(x).

A function refers to a relation which expresses relationship between two variables. It contains one value for each value of x. If there are more than one value for one value of x then it is not said to be a function.

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

To transform f(x) into g(x)  we need to follow the following steps:

  1. First subtract  3 from f(x).
  2. Then multiply the expression received from above step by 3.
  3. Next step is to add x/3 to the expression received from the above step.
  4. Now we will get the g(x)=[tex]x/3+3(x^{2} -3)[/tex].

Hence we have to use addition, subtraction and multiplication for transformation.

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