Question

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

g(x) = x − 6
g(x) = x − 2
g(x) = x + 2
g(x) = x + 6

Answer 1

Answer: The correct option is

(D)
`g(x)=x+6.`

Step-by-step explanation: Given that the following function is shifted 2 units to the right :

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

We are to write the equation when the function (i) is shifted 2 units to the right.

We know that

if a function is shifted 2 units to the right, then its x co-ordinate is reduced by 2 units.

Therefore, the equation of the new function is given by

`g(x)=f(x-2)=(x-2)+8=x+6.`

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

Option (D) is CORRECT.

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`