The correct option is A, as h(x) = f(x + 8) represents a translation of the graph of f to the right by 8 units. This occurs by adding 8 to the input (x).
For the function h(x) = f(x + 8), the transformation involves adding 8 to the input (x) of the original function f(x). When a constant is added inside the function, it causes a horizontal shift in the graph. If the constant is positive, as in this case, the graph shifts to the left. Therefore, option A correctly describes the transformation as a translation of the graph of f(x) to the right by 8 units.
This shift implies that for any given x-value in h(x), the corresponding value in f(x) occurred 8 units to the left. It's important to note that this transformation only affects the horizontal position of the graph, not its slope or vertical position.
The correct option is A. It is the graph of f translated 8 units to the right.
Complete question:
Which transformation correctly describes the graph of h if h(x) = f(x + 8) for the function f(x) = x?
A. It is the graph of f translated 8 units to the right.
B. It is the graph of f where the slope is increased by 8.
C. It is the graph of f translated 8 units up.
D. It is the graph of f translated 8 units to the left.