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

Answer:

$g(x)=x+6$

Step-by-step 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

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

$g(x)=x+6$