Question

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.

Answer 1

Option A -The graph of G(x) is the graph of F(x) shifted 6 units to the right and 3 units down.

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.

Answer 2

From the given, G(x) = F(x - 6) - 3, the graph is shifted to 6 units to the right and 3 units down. Thus, the answer is letter A. It should be noted that for horizontal shifting, negative means to the right and down for vertical shifting.