Question

Suppose that G(x)= F(x-4) which statement best compares the graph of G(x) with the graph of F(x)

Answer 1

Option A.

Explanation:

The translation is defined as

`G(x)=F(x+a)+b` .... (1)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

It is given that

`G(x)=F(x-4)` .... (2)

On comparing (1) and (2) we get

a=-4<0, So the graph of G(x) is the graph of F(x) shifted 4 units to the right.

Therefore, the correct option is A.

Answer 2

The correct option is A. The graph of g(x) is the graph of f(x) shifted 4 units to the right

Explanation:

The graph of g(x) is given equal to f(x - 4)

We need to give the statement that best compares the graph of g(x) with the graph of f(x)

Now, f(x - 4) states that the graph of g(x) is shifted 4 units to the right as compared to the graph of f(x)

Therefore, The statement that best compares the graph of g(x) with the graph of f(x) is : The graph of g(x) is the graph of f(x) shifted 4 units to the right

Hence, The correct option is A. The graph of g(x) is the graph of f(x) shifted 4 units to the right