Question

Suppose f(x) = x. Find the graph of f(x+2).

Click on the correct answer.
graph 1
graph 2
Click on each graph to enlarge it.
graph 3
graph 4

Answer 1

Hello!

The answer is:

The fourth graph.

Why?

We are given the following equation:

`f(x)=x`

Then, we need to find the graph of f(x+2) that will be equal to:

`f(x+2)=x+2`

`y=x+2`

Now, finding the x-axis interception, making "y" equal to 0, we have:

`0=x+2`

`-2=x`

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:

`y=x+2`

`y=0+2=2`

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!