Question

Place each function below in the appropriate cell to show the transformation from f to g.

Answer 1

`\begin{array}{ccc}{} & {g(x) = f(x) - 2} & {g(x) = f(x) + 2} & {f(x) = 3x^2 + 3} & {g(x) =3x^2 + 1} & {g(x) =3x^2 + 5} & {f(x) = 3x^2 - 3} & {g(x) =3x^2 -5} & {g(x) =3x^2 - 1} \ \end{array}`

Explanation:

Given

See attachment for complete question

Required

Complete the cells

For cell 1:

`f(x) = 3x^2 + 3`

Solve for
`g(x) = f(x) - 2`

Substitute
`f(x) = 3x^2 + 3`

`g(x) = 3x^2 + 3 - 2`

`g(x) = 3x^2 + 1`

For cell 2:

`f(x) = 3x^2 + 3`

Solve for
`g(x) = f(x) + 2`

Substitute
`f(x) = 3x^2 + 3`

`g(x) = 3x^2 + 3 + 2`

`g(x) = 3x^2 + 5`

For cell 3:

`f(x) = 3x^2 - 3`

Solve for
`g(x) = f(x) - 2`

Substitute
`f(x) = 3x^2 - 3`

`g(x) = 3x^2 - 3 - 2`

`g(x) = 3x^2 - 5`

For cell 4:

`f(x) = 3x^2 - 3`

Solve for
`g(x) = f(x) + 2`

Substitute
`f(x) = 3x^2 - 3`

`g(x) = 3x^2 - 3 + 2`

`g(x) = 3x^2 - 1`

So, the complete cell is:

`\begin{array}{ccc}{} & {g(x) = f(x) - 2} & {g(x) = f(x) + 2} & {f(x) = 3x^2 + 3} & {g(x) =3x^2 + 1} & {g(x) =3x^2 + 5} & {f(x) = 3x^2 - 3} & {g(x) =3x^2 -5} & {g(x) =3x^2 - 1} \ \end{array}`