Answer:
[tex]\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}[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
Complete the cells
For cell 1:
[tex]f(x) = 3x^2 + 3[/tex]
Solve for [tex]g(x) = f(x) - 2[/tex]
Substitute [tex]f(x) = 3x^2 + 3[/tex]
[tex]g(x) = 3x^2 + 3 - 2[/tex]
[tex]g(x) = 3x^2 + 1[/tex]
For cell 2:
[tex]f(x) = 3x^2 + 3[/tex]
Solve for [tex]g(x) = f(x) + 2[/tex]
Substitute [tex]f(x) = 3x^2 + 3[/tex]
[tex]g(x) = 3x^2 + 3 + 2[/tex]
[tex]g(x) = 3x^2 + 5[/tex]
For cell 3:
[tex]f(x) = 3x^2 - 3[/tex]
Solve for [tex]g(x) = f(x) - 2[/tex]
Substitute [tex]f(x) = 3x^2 - 3[/tex]
[tex]g(x) = 3x^2 - 3 - 2[/tex]
[tex]g(x) = 3x^2 - 5[/tex]
For cell 4:
[tex]f(x) = 3x^2 - 3[/tex]
Solve for [tex]g(x) = f(x) + 2[/tex]
Substitute [tex]f(x) = 3x^2 - 3[/tex]
[tex]g(x) = 3x^2 - 3 + 2[/tex]
[tex]g(x) = 3x^2 - 1[/tex]
So, the complete cell is:
[tex]\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}[/tex]
