Question

How do you obtain the graph of \(y=f(x+2)\) from the graph of \(y=f(x) ?\)

Short answer

Answer: The parameter "+2" inside the argument of the function y=f(x+2) causes a horizontal shift of the graph of y=f(x) 2 units to the left.

Step-by-step solution

Identify the transformation

In this case, the transformation involves the addition of 2 inside the function argument. This corresponds to a horizontal shift. Adding a positive number inside the parentheses will cause a shift to the left, while subtracting a positive number will cause a shift to the right.

Determine the direction of the shift

Because we have a positive number (+2) inside the argument of the function f(x), the graph of y=f(x+2) will be shifted to the left by 2 units compared to the graph of y=f(x).

Create the new graph

Starting from the graph of y=f(x), move every point on the graph 2 units to the left to obtain the graph of y=f(x+2). This means that for every point (x, f(x)) on the original graph, the corresponding point on the new graph will be (x-2, f(x+2)).

Verify the transformation

Once you have made the shift, double-check your work by ensuring that every point on the new graph is 2 units to the left of the corresponding point on the original graph. If this is the case, then you have successfully obtained the graph of y=f(x+2) from the graph of y=f(x).