Question

Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x+2) ?

The graph of g(x) is the graph of ​f(x)​ translated 2 units down.

The graph of g(x) is the graph of ​f(x)​ translated 2 units up.

The graph of g(x) is the graph of ​f(x)​ translated 2 units right.

The graph of g(x) is the graph of ​f(x)​ translated 2 units left.

Answer 1

The graph of g(x) is the graph of ​f(x)​ translated 2 units left

Explanation:

Answer 2

The graph of g(x) is the graph of ​f(x)​ translated 2 units left.

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 two units to the left.

Example: f(x) = x
`f(x+2) = x_(n+2)`

f(5) = 5 x+2 = 5

x+2-2 = 5-2

x=3 and f(3) = 3

f(5) = 3

This is so because 5 now matches to the output of two previous which is 3.