Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 11?
answer choices:
The graph of y = f(x) will shift up 11 units.
The graph of y = f(x) will shift right 11 units.
The graph of y = f(x) will shift left 11 units.
The graph of y = f(x) will shift down 11 units.
The correct answer is: The graph of y = f(x) will shift down 11 units.
To determine the effect of replacing the graph of y = f(x) with the graph of y = f(x) - 11, we need to understand the concept of graph transformations.
In general, adding or subtracting a constant value to the equation of a function shifts the graph vertically. Adding a positive constant value shifts the graph upward, while subtracting a positive constant value shifts the graph downward.
In this case, by subtracting 11 from the equation y = f(x), we are subtracting a positive constant value. This means that the graph will shift downward by 11 units. Therefore, the correct answer is:
The graph of y = f(x) will shift down 11 units.