Answer:
Option A -The graph of G(x) is the graph of F(x) shifted 6 units to the right and 3 units down.
Step-by-step explanation:
Given : G(x)=F(x-6)-3
We can compare graph of G(x) with graph of F(x) by looking at a and b values in G(x)=F(x-a)-b
where, a=6 and b=3
For the value of a :
If some unit is subtract from the x value then the graph shifted to right by that unit.
mathematically we can write,
f(x)→ f(x-a) → f(x) shift right with a units.
Therefore, in G(x)=F(x-6)-3
F(x)→ F(x-6) → F(x) shift right with 6 units.
⇒Graph of G(x) is the graph of F(x) shifted 6 units right.
For the value of b:
If some units is subtract from the function then the graph shifted downward by that unit.
mathematically we can write,
f(x)→ f(x)-b → f(x) shift down with b units.
Therefore, in G(x)=F(x-6)-3
F(x)→ F(x)-3 → F(x) shift down with 3 units.
⇒Graph of G(x) is the graph of F(x) shifted 3 units down.
Therefore, option A is correct that the graph of G(x) is the graph of F(x) shifted 6 units to the right and 3 units down.
