Question

The function f(x) = xis translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?

Answer 1

`g(x)=x+4`

Explanation:

Given

`f(x)=x`

`g(x)\rightarrow f(x)` shifted 7 units left and 3 units down

Translation Rules:

`f(x)\rightarrow f(x+c)`

If
`c>0` the function shifts
`c` units to the left.

If
`c<0` the function shifts
`c` units to the right.

`f(x)\rightarrow f(x)+c`

If
`c>0` the function shifts
`c` units to the up.

If
`c<0` the function shifts
`c` units to the down.

Applying the rules to
`f(x)`

`f(x)\rightarrow f(x+7)` [7 units left]

`f(x+7)\rightarrow f(x+7)-3` [3 units down]

∴
`g(x)=f(x+7)-3=(x+7)-3=x+7-3=x+4`

`g(x)=x+4`