Question

Suppose that the graph of a function f(x) is known. Then the graph of y=f(x-2) may be obtained by a _____ shift if the graph of f(x) _____ a distance of 2 units.

Answer 1

The graph of y=f(x-2) is obtained by a horizontal shift of the graph of f(x) to the right by 2 units.

Step-by-step explanation:

The graph of y=f(x-2) can be obtained by a horizontal shift of the graph of f(x) to the right by a distance of 2 units.

To perform a horizontal shift of a function, we replace x with x-2 in the function equation. This means that every x-coordinate of the original function is shifted 2 units to the right in the new graph.

For example, if the original function has a point (1,3), the corresponding point on the new graph would be (1+2,3) = (3,3).