Final answer:
The function h(x) = -xl applies a vertical stretch or compression to the original function f(x) = [x].
Step-by-step explanation:
To determine how the function h(x) = -xl shifts given the equation f(x) = [x], we need to understand the effect of each transformation on the original function.
The function f(x) = [x] represents the greatest integer function, which rounds down any real number x to the nearest integer less than or equal to x. It can also be visualized as a step function with vertical lines at each integer value.
The function h(x) = -xl applies a vertical stretch or compression to the original function. Specifically, if l > 1, the function is vertically compressed, and if 0 < l < 1, the function is vertically stretched.The negative sign indicates a reflection across the x-axis. Without any additional horizontal or vertical shifts, the graph of h(x) will be a mirror image of the graph of f(x), but flipped over the x-axis. This means that all the points that were above the x-axis in the parent function will now be below the x-axis by the same vertical distance.