Me suppose g(x)= f(x+3)+4. which statement best compares the graph of g(x) with the graph of f(x)? a. the graph of g(x) is shifted 3 units left and 4 units down. b. the graph of g(x) is shifted 3 units right and 4 units up. c. the graph of g(x) is shifted 3 units right and 4 units down. d. the graph of g(x) is shifted 3 united left and 4 units up.

This responds is correct! ↑

D. the graph of g(x) is shifted 3 united left and 4 units up.

Step-by-step explanation:

When a change is made inside the parenthesis to the input, the function shifts left and right. Addition shifts it left while subtraction shifts it to the right. Here it is translated three units to the left. Adding or subtracting a number outside the parenthesis will slide the function up and down. Here it is shifted 4 units up.

Example:    f(x) = x            

                   f(3) = 3                 x+3 = 3

                                               x+3-3 = 3-3

                                             x=0 and f(0) = 0

                                                 So f(0) +4 = 0+4 =4