SOLUTION: Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x − 2)? The graph of y = f(x) will shift left 2 units.

Question 1143299: Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x − 2)?
The graph of y = f(x) will shift left 2 units.
The graph of y = f(x) will shift right 2 units.
The graph of y = f(x) will shift up 2 units.
The graph of y = f(x) will shift down 2 units.
Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

right 2 units.

One nice say to picture this is to consider the functions y=x^2 and y=(x-2)^2.

The graph of y=x^2 has its vertex when x=0; the graph of y=(x-2)^2 has its vertex when (x-2) is 0 -- i.e., when x=2. Replacing x with x-2 moved the vertex (and therefore the whole graph) 2 units to the right.

Here are graphs of y=x^2 (red) and y=(x-2)^2 (green), showing the graph moved 2 units to the right:

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