Question

Suppose that G(x) = F(x + 8) + 4. 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 8 units to the right and 4 units down. B. The graph of G(x) is the graph of F(x) shifted 8 units to the left and 4 units down. C. The graph of G(x) is the graph of F(x) shifted 8 units to the left and 4 units up. D. The graph of G(x) is the graph of F(x) shifted 8 units to the right and 4 units up.

Answer 1

Answer: C. The graph of G(x) is the graph of F(x) shifted 8 units to the left and 4 units up.

Step-by-step explanation: We have parent function F(x).

And G(x) = F(x+8) + 4.

We need to determine the transformations being applied in F(x) to get G(x).

According to rules of transformations,

y = f(x+C) the function f(x) is being shifted C units left.

And for y = f(x) + D, the function f(x) is being shifted D units up.

In the given function G(x) = F(x+8) + 4 the value of C is 8 and value of D is 4.

Therefore,

F(x) is being shifted 8 units left and 4 units up.

Therefore, correct option is:

C. The graph of G(x) is the graph of F(x) shifted 8 units to the left and 4 units up.