Suppose that g(x) = f(x - 6) - 3. which statement best compares the graph of g(x) with the graph of f(x)?
a. the graph of g(x) is the graph of f(x) shifted 6 units to the right and 3 units down.
b. the graph of g(x) is the graph of f(x) shifted 6 units to the left and 3 units down.
c. the graph of g(x) is the graph of f(x) shifted 6 units to the left and 3 units up.
d. the graph of g(x) is the graph of f(x) shifted 6 units to the right and 3 units up.

 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.

do it yourself this is easy

step-by-step explanation: