Hello!
The answer is:
The fourth graph.
Why?
We are given the following equation:
[tex]f(x)=x[/tex]
Then, we need to find the graph of f(x+2) that will be equal to:
[tex]f(x+2)=x+2[/tex]
[tex]y=x+2[/tex]
Now, finding the x-axis interception, making "y" equal to 0, we have:
[tex]0=x+2[/tex]
[tex]-2=x[/tex]
Therefore, the x-axis interception point is located at (-2,0), it matches with the fourth graph.
Now, finding the y-axis interception, making "x" equal to 0, we have:
[tex]y=x+2[/tex]
[tex]y=0+2=2[/tex]
Therefore, the y-axis interception point is located at (0,2), it matches with the fourth graph.
Hence, we have that the graph of f(x+2) is the fourth graph since the second graph function cuts the x-axis at -2 and the y-axis at 2.
Have a nice day!
