Question

Write the equation of a function whose parent function, f(x) = x + 8, is shifted 2 units to the right.

Answer 1

Answer: The required equation is
`g(x)=x+6.`

Step-by-step explanation: We are given to write the equation of a function whose parent function is the following and is shifted 2 units to the right :

`f(x)=x+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

if a function is shifted a units to the right, then its x co-ordinate is reduced by a units.

Therefore, the shifted function is given by

`g(x)\\\\f(x-2)\\\\=(x-2)+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Using equation (i)}]\\\\=x+6.`

Thus, the required equation is
`g(x)=x+6.`

Answer 2

`g(x)=x+6`

Explanation:

we have

`f(x)=x+8`

If f(x) is shifted 2 units to the right

then

The rule of the translation is

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

so

`g(x)=(x-2)+8`

`g(x)=x+6`