Answer:
[tex]g(x)=x+6[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x+8[/tex]
If f(x) is shifted 2 units to the right
then
The rule of the translation is
[tex]g(x)=f(x-2)[/tex]
so
[tex]g(x)=(x-2)+8[/tex]
[tex]g(x)=x+6[/tex]
Answer: The required equation is [tex]g(x)=x+6.[/tex]
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 :
[tex]f(x)=x+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
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
[tex]g(x)\\\\f(x-2)\\\\=(x-2)+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Using equation (i)}]\\\\=x+6.[/tex]
Thus, the required equation is [tex]g(x)=x+6.[/tex]
